# American Institute of Mathematical Sciences

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The existence of weak solutions to immiscible compressible two-phase flow in porous media: The case of fields with different rock-types
July  2013, 18(5): 1253-1273. doi: 10.3934/dcdsb.2013.18.1253

## Analysis and numerical approximations of equations of nonlinear poroelasticity

 1 Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849, United States, United States

Received  August 2012 Revised  January 2013 Published  March 2013

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.
Citation: Yanzhao Cao, Song Chen, A. J. Meir. Analysis and numerical approximations of equations of nonlinear poroelasticity. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1253-1273. doi: 10.3934/dcdsb.2013.18.1253
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