Weak Galerkin method for the Biot’s consolidation model

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...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2018-03, Vol.75 (6), p.2017-2030
Main Authors: Hu, Xiaozhe, Mu, Lin, Ye, Xiu
Format: Article
Language:English
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
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Summary: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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2017.07.013