A locking free numerical approximation for quasilinear poroelasticity problems. (15th September 2020)

• Record Type: Journal Article
• Authors: Zhang, Jingyuan; Zhou, Chenguang; Cao, Yanzhao; Meir, A.J.
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 6(2020)
• Page Start: 1538
• Page End: 1554
• Publication Date: 2020-09-15
• Subjects: Poroelasticity -- Dilatation-dependent permeability -- Volumetric stress formulation -- Weak Galerkin mixed finite element method -- Finite element method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.07.011
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper is devoted to a new formulation which couples the weak Galerkin method and the finite element method for approximating solutions of the equations of quasi-static poroelasticity which model flow through elastic porous media. It is assumed that the permeability of the elastic matrix depends nonlinearly on the dilatation of the porous medium. The steady-state version of the system is recast in terms of displacement, pressure, and volumetric stress, and the well-posedness of both the continuous and discrete three-field formulations is proved. Error estimates for the proposed numerical method are obtained. These show that the method is locking free . Numerical experiments presented further demonstrate the accuracy and the locking free characteristic of the proposed numerical method.