Analysis and numerical approximations of  equations of nonlinear poroelasticity

Yanzhao Cao; Song Chen; A. J. Meir

doi:10.3934/dcdsb.2013.18.1253

Article Contents

2013, Volume 18, Issue 5: 1253-1273. Doi: 10.3934/dcdsb.2013.18.1253

This issue Previous Article The existence of weak solutions to immiscible compressible two-phase flow in porous media: The case of fields with different rock-types Next Article Finite-time quenching of competing species with constrained boundary evaporation

Analysis and numerical approximations of equations of nonlinear poroelasticity

1.
Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849

Received: July 31, 2012

Revised: December 31, 2012

Published: June 2013

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Abstract

The equations of quasi-static poroelasticity which model flow through elastic porous media are considered. It is assumed that the hydraulic conductivity depends nonlinearly on the displacement (the dilatation) of the medium. The existence of a weak solution is proved using the modified Rothe's method. Numerical approximations of solutions by the finite element method are considered. Error estimates are obtained and numerical experiments are conducted to illustrate the theoretical results, and the efficiency and accuracy of the numerical method.

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Mathematics Subject Classification: Primary: 35K51, 35K59, 65M60; Secondary: 35Q74, 35Q86, 65M15, 74F10, 76S05.

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