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This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart–Thomas spaces, specifically R T 0 for triangles and unmapped R T [ 0 ] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods. [ABSTRACT FROM AUTHOR]

DarcyLite is a Matlab toolbox developed for numerical simulations of flow and transport in porous media in two dimensions. This paper focuses on the finite element methods and the corresponding code modules for solving the Darcy equation. Specifically, four major types of finite element solvers are presented: the continuous Galerkin (CG), the discontinuous Galerkin (DG), the weak Galerkin (WG), and the mixed finite element methods (MFEM). We further discuss the main design ideas and implementation strategies in DarcyLite. Numerical examples are included to demonstrate the usage and performance of this toolbox. [ABSTRACT FROM AUTHOR]

This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow. [ABSTRACT FROM AUTHOR]

This paper presents a finite element method for solving coupled Stokes–Darcy flow problems by combining the classical Bernardi–Raugel finite elements and the recently developed Arbogast–Correa (AC) spaces on quadrilateral meshes. The novel weak Galerkin methodology is employed for discretization of the Darcy equation. Specifically, piecewise constant approximants separately defined in element interiors and on edges are utilized to approximate the Darcy pressure. The discrete weak gradients of these shape functions and the numerical Darcy velocity are established in the lowest order AC space. The Bernardi–Raugel elements (B R 1 , Q 0) are used to discretize the Stokes equations. These two types of discretizations are combined at an interface, where kinematic, normal stress, and the Beavers–Joseph–Saffman (BJS) conditions are applied. Rigorous error analysis along with numerical experiments demonstrate that the method is stable and has optimal-order accuracy. • A new finite element method with the least unknowns. • Weak Galerkin pressure unknowns on interface edges behaving similarly to Lagrange multipliers. • Rigorous error analysis for optimal order accuracy. • Examples for H(div) approximation, flow exchange across interface, and 3-domain coupling. [ABSTRACT FROM AUTHOR]

This paper presents studies on modeling and algorithms for groundwater anomaly detection. Specifically, conductivity along with four other surrogates are used for identifying anomaly in groundwater, the one-class support vector machine (1-SVM) technique is utilized for model training, and real data from Colorado Water Watch is used for testing the model and algorithms. Design of code modules in Python is briefly discussed. Since groundwater contamination rarely happens in reality, we also use synthetic data from numerical simulations of flow and transport in porous media to test this model for anomaly detection. [ABSTRACT FROM AUTHOR]