Convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media

In this paper we discuss the numerical analysis of an upscaled (core scale) model describing the transport, precipitation and dissolution of solutes in a porous medium. The particularity lies in the modeling of the reaction term, especially the dissolution term, which has a multivalued character. We consider the weak formulation for the upscaled equation and provide rigorous stability and convergence results for both the semi-discrete (time discretization) and the fully discrete scheme. In doing so, compactness arguments are employed. Keywords: Numerical analysis, reactive ¿ows, weak formulation, implicit scheme, ¿nite element discretization