$L^2$-Norm Error Bounds of Characteristics Collocation Method for Compressible Miscible Displacement in Porous Media

Abstract

A nonlinear parabolic system is derived to describe compressible miscible displacement in a porous medium in non-periodic space. The concentration is treated by a characteristics collocation method, while the pressure is treated by a finite element collocation method. Optimal order estimates in $L^2$ is derived.