Volume 32, pp. 33-48, 2008.

Analysis of the DGFEM for nonlinear convection-diffusion problems

Miloslav Feistauer and Václav Kučera

Abstract

The paper is concerned with the analysis of error estimates of the discontinuous Galerkin finite element method (DGFEM) for the numerical solution of nonstationary nonlinear convection-diffusion problems equipped with Dirichlet boundary conditions. First, the case of nonlinear diffusion as well as nonlinear convection is considered. Then, the optimal $L^{\infty}(L^2)$-error estimate is discussed in the case of nonlinear convection and linear diffusion.

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Key words

nonlinear nonstationary convection-diffusion problems, nonlinear convection, nonlinear diffusion, discontinuous Galerkin finite element method, NIPG, SIPG and IIPG versions, optimal error estimates

AMS subject classifications

65M60, 76M10

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