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Analysis and numerical approximations of equations of nonlinear poroelasticity

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


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