# On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow

Mathematica Bohemica (2002)

• Volume: 127, Issue: 2, page 163-179
• ISSN: 0862-7959

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## Abstract

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The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.

## How to cite

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Dolejší, Vít, Feistauer, Miloslav, and Schwab, Christoph. "On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow." Mathematica Bohemica 127.2 (2002): 163-179. <http://eudml.org/doc/249044>.

@article{Dolejší2002,
abstract = {The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.},
author = {Dolejší, Vít, Feistauer, Miloslav, Schwab, Christoph},
journal = {Mathematica Bohemica},
keywords = {discontinuous Galerkin finite element method; numerical flux; conservation laws; convection-diffusion problems; limiting of order of accuracy; numerical solution of compressible Euler equations; discontinuous Galerkin finite element method; numerical flux; conservation laws; convection-diffusion problems; limiting of order of accuracy; numerical solution of compressible Euler equations},
language = {eng},
number = {2},
pages = {163-179},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow},
url = {http://eudml.org/doc/249044},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Dolejší, Vít
AU - Feistauer, Miloslav
AU - Schwab, Christoph
TI - On discontinuous Galerkin methods for nonlinear convection-diffusion problems and compressible flow
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 163
EP - 179
AB - The paper is concerned with the discontinuous Galerkin finite element method for the numerical solution of nonlinear conservation laws and nonlinear convection-diffusion problems with emphasis on applications to the simulation of compressible flows. We discuss two versions of this method: (a) Finite volume discontinuous Galerkin method, which is a generalization of the combined finite volume—finite element method. Its advantage is the use of only one mesh (in contrast to the combined finite volume—finite element schemes). However, it is of the first order only. (b) Pure discontinuous Galerkin finite element method of higher order combined with a technique avoiding spurious oscillations in the vicinity of shock waves.
LA - eng
KW - discontinuous Galerkin finite element method; numerical flux; conservation laws; convection-diffusion problems; limiting of order of accuracy; numerical solution of compressible Euler equations; discontinuous Galerkin finite element method; numerical flux; conservation laws; convection-diffusion problems; limiting of order of accuracy; numerical solution of compressible Euler equations
UR - http://eudml.org/doc/249044
ER -

## References

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