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Numerical Integration in the Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems in 3D

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • V. Sobotíková

    (Czech Technical University Prague, Faculty of Electrical Engineering)

Abstract

In this paper the discontinuous Galerkin finite element method is used for the space-semidiscretization of a nonlinear nonstationary convection-diffusion problem in three dimensions. As in practical computations integrals appearing in the forms defining the approximate solution are evaluated with the use of quadrature formulae, the effect of numerical integration in the method is studied. An estimate of the error caused by the numerical integration is presented and it is shown which quadrature formulae guarantee preservation of the accuracy of the method with exact integration.

Suggested Citation

  • V. Sobotíková, 2008. "Numerical Integration in the Discontinuous Galerkin Method for Nonlinear Convection-Diffusion Problems in 3D," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 347-354, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_41
    DOI: 10.1007/978-3-540-69777-0_41
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