Convergence Analysis of Miscible Displacement in Porous Media by Mixed Finite Element and Orthogonal Collocation Methods

摘要

A nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium. A sequential implicit time-stepping procedure is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the concentration is approximated by an orthogonal collocation method. Optimal order convergence in L2 -norm is proved.