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Analysis of a BDF–DGFE scheme for nonlinear convection–diffusion problems

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Abstract

We deal with the numerical solution of a scalar nonstationary nonlinear convection–diffusion equation. We employ a combination of the discontinuous Galerkin finite element method for the space semi-discretization and the k-step backward difference formula for the time discretization. The diffusive and stabilization terms are treated implicitly whereas the nonlinear convective term is treated by a higher order explicit extrapolation method, which leads to the necessity to solve only a linear algebraic problem at each time step. We analyse this scheme and derive a priori asymptotic error estimates in the discrete L ∞(L 2)-norm and the L 2(H 1)-seminorm with respect to the mesh size h and time step τ for k = 2,3. Numerical examples verifying the theoretical results are presented.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 18675, Praha 8, Czech Republic

    Vít Dolejší & Miloslav Vlasák

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  1. Vít Dolejší
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  2. Miloslav Vlasák
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Correspondence to Vít Dolejší.

Additional information

This work is a part of the research project MSM 0021620839 financed by the Ministry of Education of the Czech Republic and was partly supported by the Grant No. 316/2006/B-MAT/MFF of the Grant Agency of the Charles University Prague. The research of M. Vlasák was supported by the project LC06052 of the Ministry of Education of the Czech Republic (Jindřich Nečas Center for Mathematical Modelling).

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Dolejší, V., Vlasák, M. Analysis of a BDF–DGFE scheme for nonlinear convection–diffusion problems. Numer. Math. 110, 405–447 (2008). https://doi.org/10.1007/s00211-008-0178-2

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  • DOI: https://doi.org/10.1007/s00211-008-0178-2

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