On the stability of the space–time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection–diffusion problems
The subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion te...
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| Published in | Journal of numerical mathematics Vol. 23; no. 3; pp. 211 - 233 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
01.09.2015
Walter de Gruyter GmbH |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1570-2820 1569-3953 |
| DOI | 10.1515/jnma-2015-0014 |
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| Abstract | The subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty are used. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. An important tool is the concept of the discrete characteristic function. Theoretical results are accompanied by numerical experiments. |
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| AbstractList | The subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty are used. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. An important tool is the concept of the discrete characteristic function. Theoretical results are accompanied by numerical experiments. |
| Author | Balázsová, Monika Hadrava, Martin Feistauer, Miloslav Kosík, Adam |
| Author_xml | – sequence: 1 givenname: Monika surname: Balázsová fullname: Balázsová, Monika email: b.moncsi@gmail.com organization: Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha – sequence: 2 givenname: Miloslav surname: Feistauer fullname: Feistauer, Miloslav organization: Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8 – sequence: 3 givenname: Martin surname: Hadrava fullname: Hadrava, Martin organization: Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8 – sequence: 4 givenname: Adam surname: Kosík fullname: Kosík, Adam organization: Charles University in Prague, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8 |
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| SubjectTerms | Boundaries Diffusion discrete characteristic function Discretization Economic models Galerkin methods Mathematical analysis Mathematical models Nonlinear convection-diffusion problems Nonlinearity space and time discretization space-time discontinuous Galerkin method Stability stability of the method |
| Title | On the stability of the space–time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection–diffusion problems |
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