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 ... read morethe 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.read less
Hu, Xiaozhe, Lin Mu, and Xiu Ye. "Weak Galerkin Method for the Biot's Consolidation Model." Computers & Mathematics with Applications 75, no. 6 (March 2018): 2017-30. https://doi.org/10.1016/j.camwa.2017.07.013.
