Analysis of local uniform grid refinement:
Abstract: "Numerical methods for time-dependent PDEs usually integrate on a fixed grid, a priori chosen for the whole time interval. Similar as a fixed stepsize, a fixed grid may be inefficient when solutions possess large local gradients. While most schemes can easily adapt the stepsize, as in...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1992
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1992,11 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Numerical methods for time-dependent PDEs usually integrate on a fixed grid, a priori chosen for the whole time interval. Similar as a fixed stepsize, a fixed grid may be inefficient when solutions possess large local gradients. While most schemes can easily adapt the stepsize, as in genuine ODE and method-of-lines schemes, the question of how to automatically adapt the grid to rapid spatial transitions is much more involved. The subject of this paper is local uniform grid refinement (LUGR) for finite-difference methods. The idea of LUGR is to cover the spatial domain with nested, finer-and-finer, locally uniform subgrids. LUGR is applicable both to stationary and time-dependent problems For time-dependent problems the local subgrids are adapted at discrete values of time to follow eventually moving transitions. The aim of this paper is to discuss, for the class of finite-difference methods under consideration, a general error analysis that shows the interplay between local truncation and interpolation errors. This analysis points the way to a theoretically optimal strategy for the local refinement, optimal in the sense that this strategy controls accumulation of interpolation errors and simultaneously strives for the spatial accuracy that would be obtained on the finest grid when used without adaptation Attention is paid to both the stationary and time-dependent case, while for time-dependent problems the emphasis lies on combining LUGR with Runge-Kutta time stepping. |
| Beschreibung: | 18 S. |
Internformat
MARC
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| 100 | 1 | |a Verwer, Jan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analysis of local uniform grid refinement |c J. G. Verwer ; R. A. Trompert |
| 264 | 1 | |a Amsterdam |c 1992 | |
| 300 | |a 18 S. | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |v 1992,11 | |
| 520 | 3 | |a Abstract: "Numerical methods for time-dependent PDEs usually integrate on a fixed grid, a priori chosen for the whole time interval. Similar as a fixed stepsize, a fixed grid may be inefficient when solutions possess large local gradients. While most schemes can easily adapt the stepsize, as in genuine ODE and method-of-lines schemes, the question of how to automatically adapt the grid to rapid spatial transitions is much more involved. The subject of this paper is local uniform grid refinement (LUGR) for finite-difference methods. The idea of LUGR is to cover the spatial domain with nested, finer-and-finer, locally uniform subgrids. LUGR is applicable both to stationary and time-dependent problems | |
| 520 | 3 | |a For time-dependent problems the local subgrids are adapted at discrete values of time to follow eventually moving transitions. The aim of this paper is to discuss, for the class of finite-difference methods under consideration, a general error analysis that shows the interplay between local truncation and interpolation errors. This analysis points the way to a theoretically optimal strategy for the local refinement, optimal in the sense that this strategy controls accumulation of interpolation errors and simultaneously strives for the spatial accuracy that would be obtained on the finest grid when used without adaptation | |
| 520 | 3 | |a Attention is paid to both the stationary and time-dependent case, while for time-dependent problems the emphasis lies on combining LUGR with Runge-Kutta time stepping. | |
| 650 | 4 | |a Differential equations, Partial | |
| 700 | 1 | |a Trompert, Ron A. |e Verfasser |4 aut | |
| 810 | 2 | |a Afdeling Numerieke Wiskunde: Report NM |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 1992,11 |w (DE-604)BV010177152 |9 1992,11 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006766720 | ||
Datensatz im Suchindex
| _version_ | 1804124586349953024 |
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| any_adam_object | |
| author | Verwer, Jan Trompert, Ron A. |
| author_facet | Verwer, Jan Trompert, Ron A. |
| author_role | aut aut |
| author_sort | Verwer, Jan |
| author_variant | j v jv r a t ra rat |
| building | Verbundindex |
| bvnumber | BV010185891 |
| ctrlnum | (OCoLC)27961158 (DE-599)BVBBV010185891 |
| format | Book |
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| id | DE-604.BV010185891 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:48:01Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006766720 |
| oclc_num | 27961158 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 18 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| record_format | marc |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM |
| spelling | Verwer, Jan Verfasser aut Analysis of local uniform grid refinement J. G. Verwer ; R. A. Trompert Amsterdam 1992 18 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1992,11 Abstract: "Numerical methods for time-dependent PDEs usually integrate on a fixed grid, a priori chosen for the whole time interval. Similar as a fixed stepsize, a fixed grid may be inefficient when solutions possess large local gradients. While most schemes can easily adapt the stepsize, as in genuine ODE and method-of-lines schemes, the question of how to automatically adapt the grid to rapid spatial transitions is much more involved. The subject of this paper is local uniform grid refinement (LUGR) for finite-difference methods. The idea of LUGR is to cover the spatial domain with nested, finer-and-finer, locally uniform subgrids. LUGR is applicable both to stationary and time-dependent problems For time-dependent problems the local subgrids are adapted at discrete values of time to follow eventually moving transitions. The aim of this paper is to discuss, for the class of finite-difference methods under consideration, a general error analysis that shows the interplay between local truncation and interpolation errors. This analysis points the way to a theoretically optimal strategy for the local refinement, optimal in the sense that this strategy controls accumulation of interpolation errors and simultaneously strives for the spatial accuracy that would be obtained on the finest grid when used without adaptation Attention is paid to both the stationary and time-dependent case, while for time-dependent problems the emphasis lies on combining LUGR with Runge-Kutta time stepping. Differential equations, Partial Trompert, Ron A. Verfasser aut Afdeling Numerieke Wiskunde: Report NM Centrum voor Wiskunde en Informatica <Amsterdam> 1992,11 (DE-604)BV010177152 1992,11 |
| spellingShingle | Verwer, Jan Trompert, Ron A. Analysis of local uniform grid refinement Differential equations, Partial |
| title | Analysis of local uniform grid refinement |
| title_auth | Analysis of local uniform grid refinement |
| title_exact_search | Analysis of local uniform grid refinement |
| title_full | Analysis of local uniform grid refinement J. G. Verwer ; R. A. Trompert |
| title_fullStr | Analysis of local uniform grid refinement J. G. Verwer ; R. A. Trompert |
| title_full_unstemmed | Analysis of local uniform grid refinement J. G. Verwer ; R. A. Trompert |
| title_short | Analysis of local uniform grid refinement |
| title_sort | analysis of local uniform grid refinement |
| topic | Differential equations, Partial |
| topic_facet | Differential equations, Partial |
| volume_link | (DE-604)BV010177152 |
| work_keys_str_mv | AT verwerjan analysisoflocaluniformgridrefinement AT trompertrona analysisoflocaluniformgridrefinement |