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.

EUDML-ID : urn:eudml:doc:287818
Mots clés:
Mots clés:

@article{702894,
     title = {An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems},
     booktitle = {Applications of Mathematics 2012},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2012},
     pages = {72-82},
     mrnumber = {MR3204401},
     zbl = {1313.65302},
     url = {http://dml.mathdoc.fr/item/702894}
}

Dolejší, Vít. An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems, dans Applications of Mathematics 2012, GDML_Books,  (2012), pp. 72-82. http://gdmltest.u-ga.fr/item/702894/