TY - JOUR
T1 - An Optimal-Order Error Estimate for an $H^1$-Galerkin Mixed Method for a Pressure Equation in Compressible Porous Medium Flow
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 132
EP - 148
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/616.html
KW - $H^1$-Galerkin mixed finite element method, optimal-order error estimates, numerical examples.
AB - <p style="text-align: justify;">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.</p>