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Los sistemas Business Intelligence (BI) permiten el acceso y el analisis de la informacion para mejorar y optimizar los procesos de toma de decision tanto en agilidad como en rendimiento de sus resultados. En el presente articulo se presenta el proceso de implantacion de un BI para la Revista DYNA. Dicha implantacion responde al interes de la revista de aumentar su factor de impacto (IF o Impact Factor) en las principales listas de impacto de revistas cientificas. La herramienta desarrollada permite la identificacion de areas, campos, autores, revisores, etc. prioritarios y favorece el apoyo de la toma de decisiones a la hora de aceptar o rechazar trabajos, estimar el impacto que pueden llegar a tener los mismos, apostar por tematicas, etc. Palabras clave: Business Intelligence, Inteligencia de Negocio, Cienciametria, Mejora del factor de impacto

Solving inverse problems is a crucial task in several applications that strongly affect our daily lives, including multiple engineering fields, military operations, and/or energy production. There exist different methods for solving inverse problems, including gradient based methods, statistics based methods, and Deep Learning (DL) methods. In this work, we focus on the latest. Specifically, we study the design of proper loss functions for dealing with inverse problems using DL. To do this, we introduce a simple benchmark problem with known analytical solution. Then, we propose multiple loss functions and compare their performance when applied to our benchmark example problem. In addition, we analyze how to improve the approximation of the forward function by: (a) considering a Hermite-type interpolation loss function, and (b) reducing the number of samples for the forward training in the Encoder-Decoder method. Results indicate that a correct design of the loss function is crucial to obtain accurate inversion results.

We present FCIRK16, a 16th-order implicit symplectic integrator for long-term high precision Solar System simulations. Our integrator takes advantage of the near-Keplerian motion of the planets around the Sun by alternating Keplerian motions with corrections accounting for the planetary interactions. Compared to other symplectic integrators (the Wisdom and Holman map and its higher order generalizations) that also take advantage of the hierarchical nature of the motion of the planets around the central star, our methods require solving implicit equations at each time-step. We claim that, despite this disadvantage, FCIRK16 is more efficient than explicit symplectic integrators for high precision simulations thanks to: (i) its high order of precision, (ii) its easy parallelization, and (iii) its efficient mixed-precision implementation which reduces the effect of round-off errors. In addition, unlike typical explicit symplectic integrators for near Keplerian problems, FCIRK16 is able to integrate problems with arbitrary perturbations (non necessarily split as a sum of integrable parts). We present a novel analysis of the effect of close encounters in the leading term of the local discretization errors of our integrator. Based on that analysis, a mechanism to detect and refine integration steps that involve close encounters is incorporated in our code. That mechanism allows FCIRK16 to accurately resolve close encounters of arbitrary bodies. We illustrate our treatment of close encounters with the application of FCIRK16 to a point mass Newtonian 15-body model of the Solar System (with the Sun, the eight planets, Pluto, and five main asteroids) and a 16-body model treating the Moon as a separate body. We also present some numerical comparisons of FCIRK16 with a state-of-the-art high order explicit symplectic scheme for 16-body model that demonstrate the superiority of our integrator when very high precision is required., Consolidated Research Group MATHMODE (IT1294-19)

The main idea of our Goal-Oriented Adaptive (GOA) strategy is based on performing global and uniform h- or p-refinements (for h- and p-adaptivity, respectively) followed by a coarsening step, where some basis functions are removed according to their estimated importance. Many Goal-Oriented Adaptive strategies represent the error in a Quantity of Interest (QoI) in terms of the bilinear form and the solution of the direct and adjoint problems. However, this is unfeasible when solving indefinite or non-symmetric problems since symmetric and positive definite forms are needed to define the inner product that guides the refinements. In this work, we provide a Goal-Oriented Adaptive (h- or p-) strategy whose error in the QoI is represented in another bilinear symmetric positive definite form than the one given by the adjoint problem. For that purpose, our Finite Element implementation employs a multi-level hierarchical data structure that imposes Dirichlet homogeneous nodes to avoid the so-called hanging nodes. We illustrate the convergence of the proposed approach for 1D Helmholtz and convection-dominated problems.

The aim of this paper is to characterize the mechanical behavior of corrugated cardboard boxes using simple models that allow an approach to the load capacity and the deformation of the boxes. This is very interesting during a box design stage, in which the box does not exist yet. On the one hand, a mathematical model of strength and deformation of boxes with different geometry is obtained from experiments according to the Box Compression Test and Edge Crush Test standards. On the second hand, a finite element simulation is proposed in which only the material elastic modulus in the compression direction is needed. For that, corrugated cardboard sheets are glued to build billets for testing, and an equivalent elastic modulus is obtained. This idea arises from the fact that the collapse of the box is given by the local bucking of the corrugated cardboard panels, due to the slenderness itself, and the properties in the compression direction are predominant. As a result, the numerical models show satisfactory agreement with experiments, concluding that it is an adequate methodology to simulate in a simple and efficient way this type of boxes built with corrugated cardboard. This research was funded by the Deusto Digital Industry Chair.

In many engineering applications, the global energy of the problem may be a quantity of limited relevance. This motivated the design of goal-oriented adaptive finite element methods (see e.g. [1,4-6]). They intend to approximate a particular Quantity of Interest (QoI) using an error estimator based on the solution of the adjoint problem to guide the refinements. In this framework, Darrigrand et al. [3] presented an alternative dual operator for the representations of the error in the QoI. In the context of hp-adaptivity, Darrigrand et al. [2] proposed an algorithm for symmetric and positive definite (SPD) problems based on performing global refinements followed by optimal unrefinements. This algorithm marks the basis functions with the lowest contributions to the energy of the solution and remove them. The resulting automatic hp-adaptive strategy employs a multi-level hierarchical data-structure proposed by Zander et al. [7]. In this presentation, we extended Darrigrand et al. [2] algorithm to non-SPD problems in the framework of goal-oriented adaptivity. To do so, we evaluate the contribution to the energy in the alternative dual operator proposed by Darrigrand et al. [3], thus, considering both the direct and the adjoint problem. As a result, we obtain an hp-adaptive algorithm for SPD and non-SPD problems in the context of goal-oriented adaptivity. We test and analyze our algorithm on two-dimensional (2D) Laplace, Helmholtz, and convection-dominated problems. We also describe the main features and limitations of the proposed method. In particular, our algorithm is robust and simple to implement; therefore, it can be used for industrial applications.

The machine tool industry, which is the starting point of all the metal producing activities, is presently undergoing rapid and continuous changes as a result of the fourth industrial revolution Industry 4.0. Manufacturing models are profoundly transforming with emerging digitalization. Smart technologies like artificial intelligence (AI), big data, the Internet of Things (IoT), digital twin, allow the machine tool companies to optimize processes, increase efficiency and reduce waste through a new phase of automation. These technologies, as well, enable the machine tool producers to reach the aim of creating products with improved performance, extended life, high reliability that are eco-efficient. Therefore, Industry 4.0 could be perceived as an invaluable opportunity for the machine tool sector, only if the sector has a competent workforce capable of handling the implementation of new business models and technological developments. The main condition to create this highly qualified workforce is reskilling and upskilling of the current workforce. Once we define the expected evolution of skills requirements, we can clarify the skills mismatch between the workers and job profiles. Only then, we can reduce them by delivering well-developed trainings. For this purpose, this article identifies the current and foreseen skills requirements demanded by the machine tool industry workforce. To this end, we generated an integrated database for the sector with the present and prospective skills needs of the metal processing sector professionals. The presented sectoral database is a fundamental structure that will make the sector acquire targeted industrial reforms. It can also be an essential instrument for machine tool companies, policymakers, academics and education or training centers to build well-designed and effective training programs to enhance the skills of the labor force This research was partly funded by (a) the European Union through the Erasmus Plus Programme (Grant Agreement No. 2018-3019/001-001, Project No. 600886-1-2018-1-DE-EPPKA2-SSA-B). (b) the HAZITEK call of the Basque Government, project acronym Adit4All and (c) Accenture, Inzu Group, Fundación Telefónica and Fundación BBK, partners of the Deusto Digital Industry Chair.

The construction sector has always occupied a strategic place in the European economy. The European construction industry suffered during the 2007&ndash, 2008 global financial crisis, and today the sector is undergoing a recovery process. Among all the construction subsectors, civil engineering has the highest growth rate. Currently, the sector has to face profound industrial changes emerging with digital transformations (Industry 4.0), sustainability, climate change and energy efficiency. To promote the growth of the civil engineering sector and accelerate the recovery, we need to create a highly qualified and competent workforce that can handle the challenges coming up with the technological progress and global competitiveness. The main condition to achieve this capable workforce is to define the expected evolution of skills requirements. For that purpose, our work focuses on identifying current and near-future key skills required by the civil engineering occupations. To achieve this, we developed an automated sectoral database for the current and near-future skills requirements of the selected professional profiles. It is our belief that this sectoral database is a fundamental framework that will guide the sector through the future changes. We also believe that our research can be used as a key tool for construction companies, policy-makers, academics and training centers to develop well-designed and efficient training programs for upskilling and reskilling the workforce.

Calculating adequate vehicle routes for collecting municipal waste is still an unsolved issue, even though many solutions for this process can be found in the literature. A gap still exists between academics and practitioners in the field. One of the apparent reasons why this rift exists is that academic tools often are not easy to handle and maintain by actual users. In this work, the problem of municipal waste collection is modeled using a simple but efficient and especially easy to maintain solution. Real data have been used, and it has been solved using a Genetic Algorithm (GA). Computations have been done in two different ways: using a complete random initial population, and including a seed in this initial population. In order to guarantee that the solution is efficient, the performance of the genetic algorithm has been compared with another well-performing algorithm, the Variable Neighborhood Search (VNS). Three problems of different sizes have been solved and, in all cases, a significant improvement has been obtained. A total reduction of 40% of itineraries is attained with the subsequent reduction of emissions and costs. This research was funded by Fundación BBK, partner of the Deusto Digital Industry Chair.

The food industry has recently faced rapid and constant changes due to the current industrial revolution, Industry 4.0, which has also profoundly altered the dynamics of the industry overall. Due to the emerging digitalisation, manufacturing models are changing through the use of smart technologies, such as robotics, Artificial Intelligence (AI), Internet of Things (IoT), machine learning, etc. They are experiencing a new phase of automation that enables innovative and more efficient processes, products and services. The introduction of these novel business models demands new professional skills requirements in the workforce of the food industry. In this work, we introduce an industry-driven proactive strategy to achieve a successful digital transformation in the food sector. For that purpose, we focus on defining the current and near-future key skills and competencies demanded by each of the professional profiles related to the food industry. To achieve this, we generated an automated database of current and future professions and competencies and skills. This database can be used as a fundamental roadmap guiding the sector through future changes caused by Industry 4.0. The interest shown by the local sectorial cluster and related entities reinforce the idea. This research will be a key tool for both academics and policy-makers to provide well-developed and better-oriented continuous training programs in order to reduce the skill mismatch between the workforce and the jobs. This research was co-funded by Fundación BBK–BBK fundazioa, partner of the Deusto Digital Industry Chair.

espanolEn este trabajo se presenta la implementacion de actividades interdisciplinares para el aprendizaje de la geometria, utilizando applets dinamicas programadas en GeoGebra. Estas actividades se desarrollan en dos asignaturas basicas de ingenieria: Algebra y Geometria y Expresion Grafica. Las actividades se han propuesto tanto en sesiones presenciales como en no presenciales fomentando la interactividad y el aprendizaje autonomo. Se ha evaluado la actividad interdisciplinar, el uso del software y la adquisicion de conocimientos por parte del alumnado. La evaluacion ha mostrado que los estudiantes valoran positivamente las tareas propuestas y la utilizacion del programa informatico elegido para desarrollarlas. Ademas, les ha facilitado la comprension y profundizacion de conceptos geometricos. Por ello, la integracion de GeoGebra en el proceso ensenanza-aprendizaje de la geometria ha sido satisfactorio, aunque el profesorado piensa que el alumnado debe ser mas consciente de la relacion existente entre las dos materias. EnglishThis paper presents the implementation of interdisciplinary activities for the learning of geometry, using dynamic applets programmed in GeoGebra. These activities are developed in two basic engineering subjects: Algebra and Geometry and Graphical Expression. The activities have been proposed both in face-to-face sessions and on-line sessions, promoting interactivity and autonomous learning. The interdisciplinary nature of the activities, the use of software and the acquisition of knowledge by students have been evaluated. The evaluation has shown that students positively value the proposed tasks and the use of the software chosen to develop them. In addition to that, it has facilitated the understanding and deepening of geometric concepts. Therefore, the integration of GeoGebra in the teaching-learning process of geometry has been satisfactory, although lecturers think that students should be more aware of the relationship between the two subjects.

In the current climate emergency context, many national and international organizations have adopted measures to integrate sustainability and Sustainable Development Goals (SDGs) in all their fields of action. Within education, steps have been taken to incorporate the perspective of sustainability at all levels. This process has also started at the university since it plays a fundamental role in the strategy for the implementation of specific policies to promote sustainability. However, sometimes it is difficult to include this type of knowledge in the curriculum, due to the lack of flexibility of the university structure or the lack of time to cover the syllabus. In this scenario, civil engineering plays a main role as a fundamental activity in the creation of services and infrastructures with a high environmental impact. The objective of this study is to show a multidisciplinary approach to working on sustainability in a transversal way in the civil engineering degree and to analyze the impact that this type of initiative can have from the learning point of view. The study shows a curricular trajectory supported by problem-based learning and project-based learning designed to promote sustainability in the practice of civil engineering. The good results obtained in the evaluation of the project and the growing incorporation of the SDGs in the final degree projects suggest that this methodology can be implemented by other university degrees.

This work presents the results obtained from a spatial modeling and analysis process on pollutants measured in the air through forty-three monitoring stations located in the three provinces of the Basque Autonomous Community (Spain). The pollutants measured correspond to the set of nitrogen oxides (nitric oxide, NO, nitrogen dioxide, NO 2, and nitrogen oxides, NO x ) and atmospheric particulate matter with a diameter less than or equal to 10 micrometers (PM 10 ). The objective of this work was to generate a map of the pollutants that exhaustively covers the entire area of the Basque Autonomous Community using geostatistical techniques, in such a way that it serves as a basis for short and midterm environmental studies.

In the present study, the influence of the sampling density on the coestimation error of a regionalized, locally stationary and geo-mining nature variable is analyzed. The case study is two-dimensional (2D) and synthetic-type, and it has been generated using a non-conditional Sequential Gaussian Simulation (SGS), with subsequent transformation to Gaussian distribution, seeking to emulate the structural behavior of the aforementioned variable. A primary and an auxiliary variable with different spatial and statistical properties are constructed using the same methodology. The collocated ordinary cokriging method has been applied, in which the auxiliary variable is spatially correlated with the primary one and it is known exhaustively. Fifteen sampling densities are extracted from the target population of the primary variable, which are compared with the simulated values after performing coestimation. The obtained results follow a potential function that indicates the mean global error (MGE) based on the sampling density percentage (SDP) ( M G E = 1 . 2366 &middot, S D P - 0 . 224 ).

In recent times, new learning methodologies known as student-based methodologies have been introduced to simplify the learning process for the students and facilitate the acquisition of skills for them. Among them, problem based learning (PBL) and project-based learning (PjBL) are widely used methods in the world of education. Real case solving (RCS) is a variant of the PBL where students solve real cases through the application of the PBL methodology. RCS seems to be a relevant approach for educators, but it has an apparently limited implementation degree at the academic level. This article presents the successful implementation of four different RCS approaches in the lecturing process in five different classes in the engineering degree of University of Deusto. The initiative has been analyzed both quantitative and qualitatively, the overall performance and success rate of the students were compared with the ones acquired from conventional teaching methods. The results were found to be promising, demonstrating a significantly better performance than the traditional teaching methodologies. The successful results encouraged the university to continue working further in this direction.

In goal-oriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In time-dependent problems, this adaptive algorithm involves solving a dual problem that runs backward in time. This process is, in general, computationally expensive in terms of memory storage. In this work, we define a pseudo-dual problem that runs forward in time. We also describe a forward-in-time adaptive algorithm that works for some specific problems. Although it is not possible to define a general dual problem running forwards in time that provides information about future states, we provide numerical evidence via one-dimensional problems in space to illustrate the efficiency of our algorithm as well as its limitations. Finally, we propose a hybrid algorithm that employs the classical backward-in-time dual problem once and then performs the adaptive process forwards in time.

The growth of the renewable energy industry is happening at a swift pace pushed, by the emergence of Industry 4.0. Smart technologies like artificial intelligence (AI), Big Data, the Internet of Things (IoT), Digital Twin (DT), etc. enable companies within the sector of renewable energies to drastically improve their operations. In this sectoral context, where upgraded sustainability standards also play a vital role, it is necessary to fulfil the human capital requirements of the imminent technological advances. This article aims to determine the current skills of the renewable energy industry workforce and to predict the upcoming skill requirements linked to a digital transition by creating a unified database that contains both types of skills. This will serve as a tool for renewable energy businesses, education centers, and policymakers to plan the training itinerary necessary to close the skills gap, as part of the sectoral strategy to achieve a competent future workforce. This research was partly funded by (a) the European Union through the Erasmus Plus Programme (Grant Agreement No. 2018-3019/001-001, Project No. 600886-1-2018-1-DE-EPPKA2-SSA-B)*, (b) the 4gune cluster, Siemens Gamesa and Aalborg University through the project “Identification of the necessary skills and competences for professionals of the future renewable energy sector”, and (c) Lantek, Inzu Group, Fundación Telefónica and Fundación BBK, partners of the Deusto Digital Industry Chair.

Due to the importance of road transport an adequate identification of the various road network levels is necessary for an efficient and sustainable management of the road infrastructure. Additionally, traffic values are key data for any pavement management system. In this work traffic volume data of 2019 in the Basque Autonomous Community (Spain) were analyzed and modeled. Having a multidimensional sample, the average annual daily traffic (AADT) was considered as the main variable of interest, which is used in many areas of the road network management. First, an exploratory analysis was performed, from which descriptive statistical information was obtained continuing with the clustering by various variables in order to standardize its behavior by translation. In a second stage, the variable of interest was estimated in the entire road network of the studied country using linear-based radial basis functions (RBFs). The estimated model was compared with the sample statistically, evaluating the estimation using cross-validation and highest-traffic sectors are defined. From the analysis, it was observed that the clustering analysis is useful for identifying the real importance of each road segment, as a function of the real traffic volume and not based on other criteria. It was also observed that interpolation methods based on linear-type radial basis functions (RBF) can be used as a preliminary method to estimate the AADT. This research was funded by The University of the Basque Country (UPV/EHU), Call for Innovation Projects “IKD i3 Laborategia” (Call 1-2020, 2019/20).

espanolCon el objeto de aportar al mejoramiento del rendimiento academico del alumnado de primer curso de dos grados de ingenieria que se imparten en la Escuela de Ingenieria de Bilbao se ha realizado un estudio pormenorizado de los resultados academicos obtenidos en cada asignatura en funcion del perfil de ingreso desde la implantacion de los nuevos planes de estudio. Ademas en cada materia se ha realizado un analisis de las carencias formativas del alumnado utilizando encuestas sobre conocimientos al inicio de la docencia de cada asignatura y a su termino que recogen, entre otras, las principales dificultades a las que se ha enfrentado el alumnado en el transcurso de la asignatura. Con la informacion obtenida en este estudio se han identificado los puntos debiles que serviran como base para el diseno de actividades formativas necesarias para compensar las carencias detectadas. EnglishVs a contribution to the improvement of the academic performance of first year students of two degrees offered at the Engineering School of Bilbao, a detailed study of the results obtained in each of the subjects based on the students’ entrance profile since the new degree programs were initiated, has been conducted. In addition to that, an analysis of the weak areas that the students have in each subject has been performed. To accomplish this, tests at the beginning and at the end of the courses have been conducted, compiling in this way the main difficulties that students face during the development of the course. With the results obtained in this study, various weak points have been detected. These findings will serve to design academic activities that compensate the detected weaknesses.

Maintenance has always been a key activity in the manufacturing industry because of its economic consequences. Nowadays, its importance is increasing thanks to the &ldquo, Industry 4.0&rdquo, or &ldquo, fourth industrial revolution&rdquo, There are more and more complex systems to maintain, and maintenance management must gain efficiency and effectiveness in order to keep all these devices in proper conditions. Within maintenance, Condition-Based Maintenance (CBM) programs can provide significant advantages, even though often these programs are complex to manage and understand. For this reason, several research papers propose approaches that are as simple as possible and can be understood by users and modified by experts. In this context, this paper focuses on CBM optimization in an industrial environment, with the objective of determining the optimal values of preventive intervention limits for equipment under corrective and preventive maintenance cost criteria. In this work, a cost-benefit mathematical model is developed. It considers the evolution in quality and production speed, along with condition based, corrective and preventive maintenance. The cost-benefit optimization is performed using a Multi-Objective Evolutionary Algorithm. Both the model and the optimization approach are applied to an industrial case.

Konposizio metodoek, Ekuazio Diferentzial Arruntak (EDAak) ebazteko oinarrizko zenbakizko integrazio-metodo bat modu egokian konposatuz emaitzak hobetzeko aukera ematen dute. Lan honetan erreparatuko diegu bigarren ordenako zehaztasuna duen oinarrizko integratzaile simetriko bat erabiliz lortzen den konposizio metodo simetrikoei. Simetrien erabilerak, ordena-baldintzak sinplifikatzeaz gain, ezezagunen kopurua gutxitzea eragiten du. Asko dira honelako metodoen koefizienteak bilatzen jardun duten autoreak. Honela, ezaguna da aipaturiko eran lortutako 8 ordenako metodorik onenak 17 atal dituela, eta 10 ordenako eta 31, 33 eta 35 ataleko metodo oso onak ere lortu direla. Lan honetan 10 ordenako eta 31 ataleko konposizio metodo simetrikoak lortzeko sortu ditugun bi teknika aurkezten dira.; Composition methods are useful when solving Ordinary Differential Equa-tions (ODEs) as they can be used to increase the order of accuracy of a given basic nu-merical integration scheme. We will focus on symmetric composition methods involv-ing some basic second order symmetric integrator with different step sizes. The introduction of symmetries into these methods simplifies the order conditions and re-duces the number of unknowns. Several authors have worked in the search of the coef-ficients of these type of methods: the best method of order 8 has 17 stages, 10-order methods of 31, 33 and 35 stages have been also found. In this work two techniques that we have built to obtain 10-order symmetric composition methods of symmetric inte-grators of s = 31 stages are explored.

Thanks to the digitalization of industry, maintenance is a trending topic. The amount of data available for analyses and optimizations in this field has increased considerably. In addition, there are more and more complex systems to maintain, and to keep all these devices in proper conditions, which requires maintenance management to gain efficiency and effectiveness. Within maintenance, Condition-Based Maintenance (CBM) programs can provide significant advantages, but often these programs are complex to manage and understand. The problem becomes more complex when equipment is analyzed in the context of a plant, where equipment can be more or less saturated, critical regarding quality, etc. Thus, this paper focuses on CBM optimization of a full industrial chain, with the objective of determining its optimal values of preventive intervention limits for equipment under economic criteria. It develops a mathematical plus discrete-event-simulation based model that takes the evolution in quality and production speed into consideration as well as condition based, corrective and preventive maintenance. The optimization process is performed using a Multi-Objective Evolutionary Algorithm. Both the model and the optimization approach are applied to an industrial case, where the data gathered by the IoT (Internet of Things) devices at edge level can detect when some premises of the CBM model are no longer valid and request a new simulation. The simulation performed in a centralized way can thus obtain new optimal values who fit better to the actual system than the existing ones. Finally, these new optimal values can be transferred to the model whenever it is necessary. The approach developed has raised the interest of a partner of the Deusto Digital Industry Chair. This research was funded by the HAZITEK call of the Basque Government, project acronym HORDAGO.

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHT-α method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 method), which we have called BDF-α. This new method is second-order accurate and with a smaller local truncation error than the BDF2, it is unconditionally stable for some values of α and it permits a parametric control of numerical dissipation.

Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the context of frequency-domain wave-propagation problems has been developed. In this paper, we extend this error representation to the case of time-domain problems. We express the entire problem in weak form in order to derive the adjoint formulation and apply goal-oriented adaptivity. One dimensional (1D) numerical results show that upper bounds for the new error representation are sharper than the classical ones. Therefore, this new error representation can be used to design more efficient goal-oriented adaptive methodologies.

Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of interest as an integral over the whole space–time domain. A full space–time variational formulation allows such representation. Most authors employ implicit time marching schemes to perform goal-oriented adaptivity as it is known that they can be reinterpreted as Galerkin methods. In this work, we consider variational forms for explicit methods in time. We derive an appropriate error representation and propose a goal-oriented adaptive algorithm in space. For that, we derive the forward Euler method in time employing a discontinuous-in-time Petrov–Galerkin formulation. In terms of time domain adaptivity, we impose the Courant–Friedrichs–Lewy condition to ensure the stability of the method. We provide some numerical results in 1D space + time for the diffusion and advection–diffusion equations to show the performance of the proposed explicit-in-time goal-oriented adaptive algorithm., The first four authors have received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska- Curie grant agreement No 777778. David Pardo, Elisabete Alberdi and Judit Muñoz-Matute were partially funded by the Basque Government Consolidated Research Group Grant IT649-13 on “Mathematical Modeling, Simulation, and Industrial Appli- cations (M2SI)” and the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), and MTM2016-81697-ERC/AEI. David Pardo has also received funding from the BCAM “Severo Ochoa” accreditation of excellence SEV-2013-0323 and the Basque Government through the BERC 2014-2017 program. Victor M. Calo was partially funded by the CSIRO Professorial Chair in Computational Geoscience at Curtin University, the Mega-grant of the Russian Federation Government (N 14.Y26.31.0013) and the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Sci- entific Industrial Research Organisation, CSIRO, of Australia. Additional support was provided at Curtin University by The Institute for Geoscience Research (TIGeR) and by the Curtin Institute for Computation. Kristoffer G. van der Zee has received funding from the School of Math- ematical Sciences at University of Nottingham. Judit Muñoz-Matute has received funding from the University of the Basque Country (UPV/EHU) grant No. PIF15/346.

Variational space-time formulations for partial di fferential equations have been of great interest in the last decades, among other things, because they allow to develop mesh-adaptive algorithms. Since it is known that implicit time marching schemes have variational structure, they are often employed for adaptivity. Previously, Galerkin formulations of explicit methods were introduced for ordinary di fferential equations employing speci fic inexact quadrature rules. In this work, we prove that the explicit Runge-Kutta methods can be expressed as discontinuous-in-time Petrov-Galerkin methods for the linear di ffusion equation. We systematically build trial and test functions that, after exact integration in time, lead to one, two, and general stage explicit Runge-Kutta methods. This approach enables us to reproduce the existing time-domain (goal-oriented) adaptive algorithms using explicit methods in time.