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42 results on '"Barrios, Tomás P."'

1. The Crouzeix-Raviart Element for non-conforming dual mixed methods: A Priori Analysis

Author

Barrios, Tomás P., Cascón, J. Manuel, and Wachtel, Andreas

Subjects
Mathematics - Numerical Analysis, 65N30 (Primary) 65N12, 65N15 (Secondary)
Abstract

Under some regularity assumptions, we report an a priori error analysis of a dG scheme for the Poisson and Stokes flow problem in their dual mixed formulation. Both formulations satisfy a Babu\v{s}ka-Brezzi type condition within the space H(div) x L2. It is well known that the lowest order Crouzeix-Raviart element paired with piecewise constants satisfies such a condition on (broken) H1 x L2 spaces. In the present article, we use this pair. The continuity of the normal component is weakly imposed by penalizing jumps of the broken H(div) component. For the resulting methods, we prove well-posedness and convergence with constants independent of data and mesh size. We report error estimates in the methods natural norms and optimal local error estimates for the divergence error. In fact, our finite element solution shares for each triangle one DOF with the CR interpolant and the divergence is locally the best-approximation for any regularity. Numerical experiments support the findings and suggest that the other errors converge optimally even for the lowest regularity solutions and a crack-problem, as long as the crack is resolved by the mesh., Comment: 25 pages, 5 tables, 8 figures

Published
2021

3. An a posteriori error analysis for an augmented discontinuous Galerkin method applied to Stokes problem.

Author

Barrios, Tomás P. and Bustinza, Rommel

Subjects
*GALERKIN methods, *A posteriori error analysis
Abstract

This paper deals with the a posteriori error analysis for an augmented mixed discontinuous formulation for the stationary Stokes problem. By considering an appropriate auxiliary problem, we derive an a posteriori error estimator. We prove that this estimator is reliable and locally efficient, and consists of just five residual terms. Numerical experiments confirm the theoretical properties of the augmented discontinuous scheme as well as of the estimator. They also show the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution. [ABSTRACT FROM AUTHOR]

Published
2024
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9. New a Posteriori Error Estimator for an Augmented Mixed FEM in Linear Elasticity

Author

Barrios, Tomás P., Behrens, Edwin M., González, María, Barth, Timothy J., Series editor, Griebel, Michael, Series editor, Keyes, David E., Series editor, Nieminen, Risto M., Series editor, Roose, Dirk, Series editor, Schlick, Tamar, Series editor, Abdulle, Assyr, editor, Deparis, Simone, editor, Kressner, Daniel, editor, Nobile, Fabio, editor, and Picasso, Marco, editor

Published
2015
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18. An a-priori error analysis for discontinuous Lagrangian finite elements applied to nonconforming dual-mixed formulations: Poisson and Stokes problems. ETNA - Electronic Transactions on Numerical Analysis

Author

Bustinza, Rommel and Barrios, Tomás P.

Subjects
discontinuous Galerkin, Lagrange shape functions, a-priori error estimates,Mathematik
Abstract

In this paper, we discuss the well-posedness of a mixed discontinuous Galerkin (DG) scheme for the Poisson and Stokes problems in 2D, considering only piecewise Lagrangian finite elements. The complication here lies in the fact that the classical Babuška-Brezzi theory is difficult to verify for low-order finite elements, so we proceed in a non-standard way. First, we prove uniqueness, and then we apply a discrete version of Fredholm's alternative theorem to ensure existence. The a-priori error analysis is done by introducing suitable projections of the exact solution. As a result, we prove that the method is convergent, and, under standard additional regularity assumptions on the exact solution, the optimal rate of convergence of the method is guaranteed.

Published
2020

26. A stabilized mixed method applied to Stokes system with nonhomogeneous source terms: The stationary case Dedicated to Prof. R. Rodríguez, on the occasion of his 65th birthday.

Author

Barrios, Tomás P., Behrens, Edwin M., and Bustinza, Rommel

Subjects
BIRTHDAYS, TERMS & phrases, ALGORITHMS
Abstract

Summary: This article is concerned with the Stokes system with nonhomogeneous source terms and nonhomogeneous Dirichlet boundary condition. First, we reformulate the problem in its dual mixed form, and then, we study its corresponding well‐posedness. Next, in order to circumvent the well‐known Babuška‐Brezzi condition, we analyze a stabilized formulation of the resulting approach. Additionally, we endow the scheme with an a posteriori error estimator that is reliable and efficient. Finally, we provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice. [ABSTRACT FROM AUTHOR]

Published
2020
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28. A POSTERIORI ERROR ANALYSIS OF AN AUGMENTED DUAL-MIXED METHOD IN LINEAR ELASTICITY WITH MIXED BOUNDARY CONDITIONS.

Author

BARRIOS, TOMÁS P., BEHRENS, EDWIN M., and GONZÁLEZ, MARÍA

Subjects
*A posteriori error analysis, *ERROR analysis in mathematics, *ELASTICITY, *FINITE element method, *LINEAR equations
Abstract

We consider an augmented mixed finite element method for the equations of plane linear elasticity with mixed boundary conditions. The method provides simultaneous approximations of the displacements, the stress tensor and the rotation. We develop an a posteriori error analysis based on the Ritz projection of the error and the use of an appropriate auxiliary function, and derive fully local reliable a posteriori error estimates that are locally efficient up to the elements that touch the Neumann boundary. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice. [ABSTRACT FROM AUTHOR]

Published
2019

30. A posteriori error analysis of an augmented mixed finite element method for Darcy flow

Author

González Taboada, María, Barrios, Tomás P., Cascón, J. Manuel, González Taboada, María, Barrios, Tomás P., and Cascón, J. Manuel

Abstract

[Abstract] We develop an a posteriori error analysis of residual type of stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual-mixed approach suitable residual type terms arising from Darcy’s law and the mass conservation equation. We derive sufficient conditions on the stabilization parameters that guarantee that the augmented variational formulation and the corresponding Galerkin scheme are well-posed. Then, we obtain a simple a posteriori error estimator and prove that it is reliable and locally efficient. Finally, we provide several numerical experiments that illustrate the theoretical results and support the use of the corresponding adaptive algorithm in practice.

Published
2015

31. Low cost a posteriori error estimators for an augmented mixed FEM in linear elasticity

Author

González Taboada, María, Barrios, Tomás P., Behrens, Edwin M., González Taboada, María, Barrios, Tomás P., and Behrens, Edwin M.

Abstract

[Abstract] We consider an augmented mixed finite element method applied to the linear elasticity problem and derive a posteriori error estimators that are simpler and easier to implement than the ones available in the literature. In the case of homogeneous Dirichlet boundary conditions, the new a posteriori error estimator is reliable and locally efficient, whereas for non-homogeneous Dirichlet boundary conditions, we derive an a posteriori error estimator that is reliable and satisfies a quasi-efficiency bound. Numerical experiments illustrate the performance of the corresponding adaptive algorithms and support the theoretical results.

Published
2014

33. A posteriori error analysis of an augmented mixed formulation in linear elasticity with mixed and Dirichlet boundary conditions

Author

González Taboada, María, Barrios, Tomás P., Behrens, Edwin M., González Taboada, María, Barrios, Tomás P., and Behrens, Edwin M.

Abstract

[Abstract] We develop a residual-based a posteriori error analysis for the augmented mixed methods introduced in and for the problem of linear elasticity in the plane. We prove that the proposed a posteriori error estimators are both reliable and efficient. Numerical experiments confirm these theoretical properties and illustrate the ability of the corresponding adaptive algorithms to localize the singularities and large stress regions of the solutions.

Published
2011

34. A residual based a posteriori error estimator for an augmented mixed finite element method in linear elasticity

Author

González Taboada, María, Barrios, Tomás P., Gatica, Gabriel N., Heuer, Norbert, González Taboada, María, Barrios, Tomás P., Gatica, Gabriel N., and Heuer, Norbert

Abstract

[Abstract] In this paper we develop a residual based a posteriori error analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriori error estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reported.

Published
2006

40. A priori and a posteriori error analyses of an augmented discontinuous Galerkin formulation.

Author

BARRIOS, TOMÁS P. and BUSTINZA, ROMMEL

Subjects
*GALERKIN methods, *LEAST squares, *BOUNDARY value problems, *ALGORITHMS, *EQUATIONS
Abstract

We use Galerkin least squares terms to develop a more general stabilized discontinuous Galerkin method for elliptic problems in the plane with mixed boundary conditions. The unique solvability and optimal rate of convergence of this scheme, with respect to the h-version, are established. Furthermore, we include the corresponding a posteriori error analysis, which results in a reliable and efficient estimator. Finally, we present several numerical examples that show the capability of the adaptive algorithm to localize the singularities, confirming the theoretical properties of the a posteriori error estimate. [ABSTRACT FROM PUBLISHER]

Published
2010
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41. A residual based A POSTERIORIerror estimator for an augmented mixed finite element method in linear elasticity

Author

Barrios, Tomás P., Gatica, Gabriel N., González, María, and Heuer, Norbert

Abstract

In this paper we develop a residual based a posteriorierror analysis for an augmented mixed finite element method applied to the problem of linear elasticity in the plane. More precisely, we derive a reliable and efficient a posteriorierror estimator for the case of pure Dirichlet boundary conditions. In addition, several numerical experiments confirming the theoretical properties of the estimator, and illustrating the capability of the corresponding adaptive algorithm to localize the singularities and the large stress regions of the solution, are also reported.

Published
2006
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42. Nutritional and Food Protection against Epidemic Emerging Neuropathy. Epidemiological Findings in the Unique Disease-free Urban Area of Cuba

Author

Barnouin, Jacques, Barrios, Tomás Verdura, Chassagne, Michelle, Cristiá, Rafael Pérez, Arnaud, Josiane, Mestre, Pedro Fleites, Montoya, María Esther, and Favier, Alain

Abstract

A survey was conducted through the SECUBA (SEguridad alimentaria en CUba y Buena Alimentación) research program in Cuban healthy smokers living in Guantánamo and in Havana. The aim of the survey was to investigate biological and nutritional factors connected with the occurrence of zero epidemic neuropathy (EN) observed in Guantánamo urban area since the disease emerged in Cuba. Blood riboflavin status and carotenoid and selenium concentrations were higher in Guantánamo than in Havana smokers. Food dietary quantities of plantain banana, pepper (Capsicum spp.), bovine meat and milk products were higher in Guantánamo. Inversely, foods rich in cholesterol, especially eggs, were more consumed in Havana. Through riboflavin, carotenoid and selenium contents and specific antioxidants substances (indoleamines, capsaicin), the foods more consumed in Guantánamo could be considered as EN protective factors. Disease protective effects could be exerted via enhancement of defence mechanisms against free radical damage and related mechanisms focused on redox recycling of glutathione and local protection from carotenoids. Finally, the results of the present study should help Cuba, through a better EN control, to improve long-term food safety and define healthier dietary habits.

Published
2001
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