An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems

Dolejší, Vít. "An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems." Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012. 72-82. <http://eudml.org/doc/287818>.

@inProceedings{Dolejší2012,
abstract = {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.},
author = {Dolejší, Vít},
booktitle = {Applications of Mathematics 2012},
keywords = {discontinuous Galerkin method; $hp$-adaptation; residuum estimator; regularity indicator; mesh refinement; stationary nonlinear convection-diffusion problems; error estimation; numerical experiments},
location = {Prague},
pages = {72-82},
publisher = {Institute of Mathematics AS CR},
title = {An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems},
url = {http://eudml.org/doc/287818},
year = {2012},
}

TY - CLSWK
AU - Dolejší, Vít
TI - An adaptive $hp$-discontinuous Galerkin approach for nonlinear convection-diffusion problems
T2 - Applications of Mathematics 2012
PY - 2012
CY - Prague
PB - Institute of Mathematics AS CR
SP - 72
EP - 82
AB - 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.
KW - discontinuous Galerkin method; $hp$-adaptation; residuum estimator; regularity indicator; mesh refinement; stationary nonlinear convection-diffusion problems; error estimation; numerical experiments
UR - http://eudml.org/doc/287818
ER -