An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow
Year: 2012
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 132–148
Abstract
We present an $H^1$-Galerkin mixed finite element method for the solution of a nonlinear parabolic pressure equation, which arises in the mathematical models for describing a compressible fluid flow process in subsurface porous media. The method possesses the advantages of mixed finite element methods while avoiding directly inverting the permeability tensor, which is important especially in a low permeability zone. We conducted theoretical analysis to study the existence and uniqueness of the numerical solutions of the scheme and prove an optimal-order error estimate for the method. Numerical experiments are performed to justify the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-IJNAM-616
International Journal of Numerical Analysis and Modeling, Vol. 9 (2012), Iss. 1 : pp. 132–148
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: $H^1$-Galerkin mixed finite element method optimal-order error estimates numerical examples.