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

Vít Dolejší; Miloslav Feistauer; Christoph Schwab

Mathematica Bohemica (2002)

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

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topDolejší, 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 -

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