Weak Galerkin finite element method for Biot's consolidation problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:330

Article

Chen, Yumei¹  Chen, Gang²  Xie, Xiaoping² 

[1] China West Normal Univ, Coll Math & Informat, Nanchong 637009, Peoples R China

[2] Sichuan Univ, Sch Math, Chengdu 610064, Sichuan, Peoples R China

关键词: Finite element method;    Biot's consolidation problem;    Weak Galerkin method;   

DOI  :  10.1016/j.cam.2017.09.019

来源: Elsevier

【 摘 要 】

In this paper, a fully discrete weak Galerkin (WG) finite element method is proposed to solve Biot's consolidation problem, where weakly defined gradient and divergence operators over discontinuous functions are introduced. P-l-P-l (l >= 1) finite element combination is used for the displacement and pressure approximations in the interior of the elements, and P-l-Pl-1 combination for the corresponding trace approximations on the interfaces of the finite element partition. The existence and uniqueness of the discrete linear system at each time step is derived, and error estimates for the approximation of displacement and pressure are obtained. Numerical experiments confirm the theoretical results and show that the proposed WG method is capable of overcoming pressure oscillations. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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