Weak Galerkin method for the Biot’s consolidation model

• Published in: Computers & mathematics with applications (1987) Vol. 75; no. 6; pp. 2017 - 2030
• Main Authors: Hu, Xiaozhe, Mu, Lin, Ye, Xiu
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.03.2018; Elsevier BV; Elsevier
• Subjects: Approximation; Biot’s consolidation model; Consolidation; Discretization; Eulers equations; Finite element analysis; Finite element method; Galerkin method; Mathematical analysis; Mathematical models; MATHEMATICS AND COMPUTING; Numerical analysis; Studies; Weak Galerkin finite elements method; Well posed problems; Finite element method; Weak Galerkin finite elements method; Biot’s consolidation model
• ISSN: 0898-1221; 1873-7668; 1873-7668
• DOI: 10.1016/j.camwa.2017.07.013

We develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure without special treatment. Numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.