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A Priori Error Estimates for DGFEM Applied to Nonstationary Nonlinear Convection–Diffusion Equation

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • J. Hozman

    (Charles University Prague, Department of Numerical Mathematics, Faculty of Mathematics and Physics)

  • V. Dolejší

    (Charles University Prague, Department of Numerical Mathematics, Faculty of Mathematics and Physics)

Abstract

We deal with a numerical solution of a scalar nonstationary convection–diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier–Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method (DGFEM) with several variants of the interior penalty, namely nonsymmetric (NIPG), symmetric (SIPG) and incomplete (IIPG) types of stabilizations of diffusion terms. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we recall a priori hp error estimates in the L 2-norm and in the H 1-seminorm. A set of numerical experiments evaluating the experimental orders of convergence in the dependence on the polynomial degree of approximation and used type of stabilization is presented.

Suggested Citation

  • J. Hozman & V. Dolejší, 2010. "A Priori Error Estimates for DGFEM Applied to Nonstationary Nonlinear Convection–Diffusion Equation," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 459-467, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_49
    DOI: 10.1007/978-3-642-11795-4_49
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