Weak Galerkin method for the Biot’s consolidation model

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

doi:10.1016/j.camwa.2017.07.013

Title: Weak Galerkin method for the Biot’s consolidation model

Journal Article · Thu Mar 01 00:00:00 EST 2018 · Computers and Mathematics with Applications (Oxford)

DOI:https://doi.org/10.1016/j.camwa.2017.07.013· OSTI ID:1854979

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, 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. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: ERKJE45; AC05-00OR22725

OSTI ID:: 1854979

Alternate ID(s):: OSTI ID: 1394349; OSTI ID: 1582708

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 75 Journal Issue: 6; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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Cited by: 19 works

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References (39)

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