Weak Galerkin method for the Biot's consolidation model. (15th March 2018)

• Record Type: Journal Article
• Authors: Hu, Xiaozhe; Mu, Lin; Ye, Xiu
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 6(2018)
• Page Start: 2017
• Page End: 2030
• Publication Date: 2018-03-15
• Subjects: Biot's consolidation model -- Finite element method -- Weak Galerkin finite elements method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.07.013
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.