Analysis of the discontinuous Galerkin method for nonlinear convection–diffusion problems
The subject-matter is the analysis of the discontinuous Galerkin finite element method applied to a nonlinear convection–diffusion problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. This allows us to consider general polyhedral elements with mutuall...
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| Published in | Computer methods in applied mechanics and engineering Vol. 194; no. 25; pp. 2709 - 2733 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.07.2005
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0045-7825 1879-2138 |
| DOI | 10.1016/j.cma.2004.07.017 |
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| Abstract | The subject-matter is the analysis of the discontinuous Galerkin finite element method applied to a nonlinear convection–diffusion problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. This allows us to consider general polyhedral elements with mutually disjoint interiors. We do not require their convexity, but assume only that they are star-shaped. We present an error analysis for the case of a nonsymmetric discretization of diffusion terms. Theoretical results are accompanied by numerical experiments. |
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| AbstractList | The subject-matter is the analysis of the discontinuous Galerkin finite element method applied to a nonlinear convection-diffusion problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. This allows us to consider general polyhedral elements with mutually disjoint interiors. We do not require their convexity, but assume only that they are star-shaped. We present an error analysis for the case of a nonsymmetric discretization of diffusion terms. Theoretical results are accompanied by numerical experiments. |
| Author | Sobotíková, V. Dolejší, V. Feistauer, M. |
| Author_xml | – sequence: 1 givenname: V. surname: Dolejší fullname: Dolejší, V. email: dolejsi@karlin.mff.cuni.cz organization: Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 186 75 Praha, Czech Republic – sequence: 2 givenname: M. surname: Feistauer fullname: Feistauer, M. email: feist@karlin.mff.cuni.cz organization: Faculty of Mathematics and Physics, Charles University Prague, Sokolovská 83, 186 75 Praha, Czech Republic – sequence: 3 givenname: V. surname: Sobotíková fullname: Sobotíková, V. email: sobotik@math.feld.cvut.cz organization: Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Praha 6, Czech Republic |
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| Cites_doi | 10.1002/(SICI)1097-0363(19990915)31:1<79::AID-FLD956>3.0.CO;2-C 10.1007/s100920200000 10.1006/jcph.1997.5454 10.1006/jcph.1996.5572 10.21136/MB.2002.134171 10.1016/S0045-7825(01)00318-8 10.1137/S0036142997314695 10.1051/m2an:1999159 10.1137/S0036142900374111 10.1016/S0378-4754(02)00087-3 |
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| Keywords | 65M15 Nonsymmetric stabilization of diffusive terms Asymptotic error estimates Discontinuous Galerkin finite element method Interior and boundary penalty 28 Nonlinear convection–diffusion equation 65M60 Numerical experiments 65M12 20 86 Discontinuity Error estimation Stabilization Nonlinear convection-diffusion equation Convection diffusion equation Experimental study Galerkin-Petrov method Finite element method Polyhedron Modelling Asymptotic approximation Convexity Non linear effect |
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| SubjectTerms | Asymptotic error estimates Discontinuous Galerkin finite element method Exact sciences and technology Fluid dynamics Fundamental areas of phenomenology (including applications) General theory Interior and boundary penalty Nonlinear convection–diffusion equation Nonsymmetric stabilization of diffusive terms Numerical experiments Physics Turbulence simulation and modeling Turbulent flows, convection, and heat transfer |
| Title | Analysis of the discontinuous Galerkin method for nonlinear convection–diffusion problems |
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