Convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media
Kundan Kumar, I. Pop, Florin A. Radu · TU/e Research Portal · 2012
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