Analysis of the implicit Euler local uniform grid refinement method:
Abstract: "The subject of the paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems the solution of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and dis...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1990
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1990,11 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The subject of the paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems the solution of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and disappearing layers. An adaptive grid method is analysed that refines the space grid locally around sharp spatial transitions, so as to avoid discretization on a very fine grid over the entire physical domain. This method is based on the techniques called static-regridding and local uniform grid refinement. Static-regridding means that in the course of the time evolution the space grid is adapted at discrete times Local uniform grid refinement means that the actual adaptation of the space grid takes place using nested locally uniformly refined grids. These uniform subgrids possess non physical boundaries and on each of these subgrids an integration is carried out. The present paper concentrates on stability and error analysis while using the implicit Euler method for time integration. Maximum norm stability and convergence results are proved for a certain class of linear and nonlinear PDE's The central issue hereby is a refinement condition with a refinement strategy that distributes spatial interpolation and discretization errors in such a way that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation. The analysis is confirmed with a numerical illustration. |
| Beschreibung: | 43 S. |
Internformat
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| 100 | 1 | |a Trompert, Ron A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis of the implicit Euler local uniform grid refinement method |c R. A. Trompert ; J. G. Verwer |
| 264 | 1 | |a Amsterdam |c 1990 | |
| 300 | |a 43 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1990,11 | |
| 520 | 3 | |a Abstract: "The subject of the paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems the solution of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and disappearing layers. An adaptive grid method is analysed that refines the space grid locally around sharp spatial transitions, so as to avoid discretization on a very fine grid over the entire physical domain. This method is based on the techniques called static-regridding and local uniform grid refinement. Static-regridding means that in the course of the time evolution the space grid is adapted at discrete times | |
| 520 | 3 | |a Local uniform grid refinement means that the actual adaptation of the space grid takes place using nested locally uniformly refined grids. These uniform subgrids possess non physical boundaries and on each of these subgrids an integration is carried out. The present paper concentrates on stability and error analysis while using the implicit Euler method for time integration. Maximum norm stability and convergence results are proved for a certain class of linear and nonlinear PDE's | |
| 520 | 3 | |a The central issue hereby is a refinement condition with a refinement strategy that distributes spatial interpolation and discretization errors in such a way that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation. The analysis is confirmed with a numerical illustration. | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Mathematical analysis | |
| 700 | 1 | |a Verwer, Jan |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1990,11 |w (DE-604)BV010177152 |9 1990,11 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006769435 | ||
Datensatz im Suchindex
| _version_ | 1804124590807449600 |
|---|---|
| any_adam_object | |
| author | Trompert, Ron A. Verwer, Jan |
| author_facet | Trompert, Ron A. Verwer, Jan |
| author_role | aut aut |
| author_sort | Trompert, Ron A. |
| author_variant | r a t ra rat j v jv |
| building | Verbundindex |
| bvnumber | BV010188985 |
| ctrlnum | (OCoLC)23947185 (DE-599)BVBBV010188985 |
| format | Book |
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| id | DE-604.BV010188985 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:05Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006769435 |
| oclc_num | 23947185 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 43 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Trompert, Ron A. Verfasser aut Analysis of the implicit Euler local uniform grid refinement method R. A. Trompert ; J. G. Verwer Amsterdam 1990 43 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1990,11 Abstract: "The subject of the paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems the solution of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and disappearing layers. An adaptive grid method is analysed that refines the space grid locally around sharp spatial transitions, so as to avoid discretization on a very fine grid over the entire physical domain. This method is based on the techniques called static-regridding and local uniform grid refinement. Static-regridding means that in the course of the time evolution the space grid is adapted at discrete times Local uniform grid refinement means that the actual adaptation of the space grid takes place using nested locally uniformly refined grids. These uniform subgrids possess non physical boundaries and on each of these subgrids an integration is carried out. The present paper concentrates on stability and error analysis while using the implicit Euler method for time integration. Maximum norm stability and convergence results are proved for a certain class of linear and nonlinear PDE's The central issue hereby is a refinement condition with a refinement strategy that distributes spatial interpolation and discretization errors in such a way that the spatial accuracy obtained is comparable to the spatial accuracy on the finest grid if this grid would be used without any adaptation. The analysis is confirmed with a numerical illustration. Differential equations, Partial Mathematical analysis Verwer, Jan Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1990,11 (DE-604)BV010177152 1990,11 |
| spellingShingle | Trompert, Ron A. Verwer, Jan Analysis of the implicit Euler local uniform grid refinement method Differential equations, Partial Mathematical analysis |
| title | Analysis of the implicit Euler local uniform grid refinement method |
| title_auth | Analysis of the implicit Euler local uniform grid refinement method |
| title_exact_search | Analysis of the implicit Euler local uniform grid refinement method |
| title_full | Analysis of the implicit Euler local uniform grid refinement method R. A. Trompert ; J. G. Verwer |
| title_fullStr | Analysis of the implicit Euler local uniform grid refinement method R. A. Trompert ; J. G. Verwer |
| title_full_unstemmed | Analysis of the implicit Euler local uniform grid refinement method R. A. Trompert ; J. G. Verwer |
| title_short | Analysis of the implicit Euler local uniform grid refinement method |
| title_sort | analysis of the implicit euler local uniform grid refinement method |
| topic | Differential equations, Partial Mathematical analysis |
| topic_facet | Differential equations, Partial Mathematical analysis |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT trompertrona analysisoftheimpliciteulerlocaluniformgridrefinementmethod AT verwerjan analysisoftheimpliciteulerlocaluniformgridrefinementmethod |