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A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Emmanuil H. Georgoulis

    (University of Leicester, Department of Mathematics)

  • Omar Lakkis

    (University of Sussex, Department of Mathematics)

Abstract

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the hp-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.

Suggested Citation

  • Emmanuil H. Georgoulis & Omar Lakkis, 2010. "A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 351-358, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_37
    DOI: 10.1007/978-3-642-11795-4_37
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