Convergence analysis of mixed numerical schemes for reactive flow in a porous medium

K. Kumar, I.S. Pop, F.A. Radu

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    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. Keywords: numerical analysis, reactive flows, weak formulation, implicit scheme, mixed finite element discretization
    Original languageEnglish
    Pages (from-to)2283-2308
    Number of pages26
    JournalSIAM Journal on Numerical Analysis
    Volume51
    Issue number4
    DOIs
    Publication statusPublished - 2013

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