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Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism

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Abstract

In this work, we apply a time-space adaptive discontinuous Galerkin method using the elliptic reconstruction technique with a robust (in Péclet number) elliptic error estimator in space, for the convection dominated parabolic problems with non-linear reaction mechanisms. We derive a posteriori error estimators in the \(L^{\infty }(L^2)+L^2(H^1)\)-type norm using backward Euler in time and discontinuous Galerkin (symmetric interior penalty Galerkin) in space. Numerical results for advection dominated reactive transport problems in homogeneous and heterogeneous media demonstrate the performance of the time-space adaptive algorithm.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Bülent Karasözen

  2. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Murat Uzunca

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  1. Bülent Karasözen
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  2. Murat Uzunca
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Correspondence to Bülent Karasözen.

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Karasözen, B., Uzunca, M. Time-space adaptive discontinuous Galerkin method for advection-diffusion equations with non-linear reaction mechanism. Int J Geomath 5, 255–288 (2014). https://doi.org/10.1007/s13137-014-0067-z

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  • DOI: https://doi.org/10.1007/s13137-014-0067-z

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