An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow

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.