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

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

    Research output: Book/ReportReportAcademic

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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 has a particular, multi-valued 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 time. More precisely, we use the lowest order Raviart-Thomas elements. As an intermediate step we consider also a semi-discrete mixed variational formulation (continuous in space). We analyse 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.
    Original languageEnglish
    Place of PublicationEindhoven
    PublisherTechnische Universiteit Eindhoven
    Number of pages28
    Publication statusPublished - 2012

    Publication series

    NameCASA-report
    Volume1220
    ISSN (Print)0926-4507

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