Finite element approximation of mass transfer in a porous medium with non equilibrium phase change

Abstract

A finite element approximations with an implicit Euler scheme is analyzed. This involves numerical integration of a semi-linear parabolic-differential inclusion arising in a model of reactive mass transport in porous media with a dissolution/precipitation process. The model is composed of parabolic equations and variational inequalities. Equations are coupled by non-linear terms. We prove the existence of solutions for the approximated problem and the convergence of the scheme towards the solution of the continuous Problem