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This content will become publicly available on August 23, 2018

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

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.
Authors:
 [1] ; ORCiD logo [2] ;  [3]
  1. Tufts Univ., Medford, MA (United States). Department of Mathematics
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
  3. University of Arkansas at Little Rock, Little Rock, AR (United States). Department of Mathematics and Statistics
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 75; Journal Issue: 6; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Biot’s consolidation model; Finite element method; Weak Galerkin finite elements method
OSTI Identifier:
1394349