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Article

Dolejší, Vít
An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 72-82
MSC: 35J60, 65N15, 65N30, 65N50 | MR 3204401 | Zbl 1313.65302
Keywords:
discontinuous Galerkin method; $hp$-adaptation; residuum estimator; regularity indicator; mesh refinement; stationary nonlinear convection-diffusion problems; error estimation; numerical experiments
Summary:
We deal with a numerical solution of nonlinear convection-diffusion equations with the aid of the discontinuous Galerkin method (DGM). We propose a new $hp$-adaptation technique, which is based on a combination of a residuum estimator and a regularity indicator. The residuum estimator as well as the regularity indicator are easily evaluated quantities without the necessity to solve any local problem and/or any reconstruction of the approximate solution. The performance of the proposed $hp$-DGM is demonstrated.
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