Convergence Analysis of Mixed Numerical Schemes for Reactive Flow in a Porous Medium

Abstract

This paper deals with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The solutes are transported by advection and diffusion and undergo precipitation and dissolution. The reaction term and, in particular, the dissolution term have a particular, multivalued character, which leads to stiff dissolution fronts. We consider the Euler implicit method for the temporal discretization and the mixed finite element for the discretization in space. More precisely, we use the lowest order Raviart--Thomas elements. As an intermediate step we consider also a semidiscrete mixed variational formulation (continuous in space). We analyze the numerical schemes and prove the convergence to the continuous formulation. Apart from the proof for the convergence, this also yields an existence proof for the solution of the model in mixed variational formulation. Numerical experiments are performed to study the convergence behavior.