Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation

Hozman, Jiří, and Dolejší, Vít. "Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation." Programs and Algorithms of Numerical Mathematics. Prague: Institute of Mathematics AS CR, 2008. 97-102. <http://eudml.org/doc/271286>.

@inProceedings{Hozman2008,
abstract = {We deal with a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we introduce a priori error estimates in the $L^\infty (0,T; L^2(\Omega ))$-norm and in the $L^2(0,T; H^1(\Omega ))$-seminorm. A sketch of the proof is presented.},
author = {Hozman, Jiří, Dolejší, Vít},
booktitle = {Programs and Algorithms of Numerical Mathematics},
location = {Prague},
pages = {97-102},
publisher = {Institute of Mathematics AS CR},
title = {Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation},
url = {http://eudml.org/doc/271286},
year = {2008},
}

TY - CLSWK
AU - Hozman, Jiří
AU - Dolejší, Vít
TI - Analysis of the discontinuous Galerkin finite element method applied to a scalar nonlinear convection-diffusion equation
T2 - Programs and Algorithms of Numerical Mathematics
PY - 2008
CY - Prague
PB - Institute of Mathematics AS CR
SP - 97
EP - 102
AB - We deal with a scalar nonstationary convection-diffusion equation with nonlinear convective as well as diffusive terms which represents a model problem for the solution of the system of the compressible Navier-Stokes equations describing a motion of viscous compressible fluids. We present a discretization of this model equation by the discontinuous Galerkin finite element method. Moreover, under some assumptions on the nonlinear terms, domain partitions and the regularity of the exact solution, we introduce a priori error estimates in the $L^\infty (0,T; L^2(\Omega ))$-norm and in the $L^2(0,T; H^1(\Omega ))$-seminorm. A sketch of the proof is presented.
UR - http://eudml.org/doc/271286
ER -