Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions

Oto Havle; Vít Dolejší; Miloslav Feistauer

Applications of Mathematics (2010)

  • Volume: 55, Issue: 5, page 353-372
  • ISSN: 0862-7940

Abstract

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The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation error in the approximation of the nonlinear convective terms. The estimate of this error allows to analyse the error estimate of the method. The results obtained represent the completion and extension of the analysis from V. Dolejší, M. Feistauer, Numer. Funct. Anal. Optim. 26 (2005), 349–383, where the truncation error in the approximation of the nonlinear convection terms was proved only in the case when the Dirichlet boundary condition on the whole boundary of the computational domain was considered.

How to cite

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Havle, Oto, Dolejší, Vít, and Feistauer, Miloslav. "Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions." Applications of Mathematics 55.5 (2010): 353-372. <http://eudml.org/doc/116467>.

@article{Havle2010,
abstract = {The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation error in the approximation of the nonlinear convective terms. The estimate of this error allows to analyse the error estimate of the method. The results obtained represent the completion and extension of the analysis from V. Dolejší, M. Feistauer, Numer. Funct. Anal. Optim. 26 (2005), 349–383, where the truncation error in the approximation of the nonlinear convection terms was proved only in the case when the Dirichlet boundary condition on the whole boundary of the computational domain was considered.},
author = {Havle, Oto, Dolejší, Vít, Feistauer, Miloslav},
journal = {Applications of Mathematics},
keywords = {nonlinear convection-diffusion equation; mixed Dirichlet-Neumann conditions; discontinuous Galerkin finite element method; method of lines; nonconforming meshes; NIPG; SIPG; IIPG versions; error estimate; space semidiscretization; nonlinear convection-diffusion equation; mixed Dirichlet-Neumann conditions; discontinuous Galerkin finite element method; method of lines; nonconforming mesh; NIPG version; SIPG version; IIPG version; error estimate; space semidiscretization},
language = {eng},
number = {5},
pages = {353-372},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions},
url = {http://eudml.org/doc/116467},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Havle, Oto
AU - Dolejší, Vít
AU - Feistauer, Miloslav
TI - Discontinuous Galerkin method for nonlinear convection-diffusion problems with mixed Dirichlet-Neumann boundary conditions
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 5
SP - 353
EP - 372
AB - The paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. General nonconforming meshes are used and the NIPG, IIPG and SIPG versions of the discretization of diffusion terms are considered. The main attention is paid to the impact of the Neumann boundary condition prescribed on a part of the boundary on the truncation error in the approximation of the nonlinear convective terms. The estimate of this error allows to analyse the error estimate of the method. The results obtained represent the completion and extension of the analysis from V. Dolejší, M. Feistauer, Numer. Funct. Anal. Optim. 26 (2005), 349–383, where the truncation error in the approximation of the nonlinear convection terms was proved only in the case when the Dirichlet boundary condition on the whole boundary of the computational domain was considered.
LA - eng
KW - nonlinear convection-diffusion equation; mixed Dirichlet-Neumann conditions; discontinuous Galerkin finite element method; method of lines; nonconforming meshes; NIPG; SIPG; IIPG versions; error estimate; space semidiscretization; nonlinear convection-diffusion equation; mixed Dirichlet-Neumann conditions; discontinuous Galerkin finite element method; method of lines; nonconforming mesh; NIPG version; SIPG version; IIPG version; error estimate; space semidiscretization
UR - http://eudml.org/doc/116467
ER -

References

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