Local corrections for eliminating the pollution effect of reentrant corners:
Abstract: "The accurate numerical solution of elliptic partial differential equations with singular solutions is particularly difficult: The error increases all over the solution domain by the so-called pollution effect. This paper examines local corrections, where only few of the discrete equa...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
München
1989
|
| Schriftenreihe: | Technische Universität <München>: TUM
8901 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "The accurate numerical solution of elliptic partial differential equations with singular solutions is particularly difficult: The error increases all over the solution domain by the so-called pollution effect. This paper examines local corrections, where only few of the discrete equations must be modified, independent of the meshsize. Using these modifications, the pollution effect can be suppressed, so that [formula] accuracy can be obtained by linear finite elements. The proof is based on the variation formulation and will be outlined for the case of Poisson's equation with reentrant corners. This generalizes previous results based on finite difference approximations on equidistant grids Applications of this correction technique within the multigrid method will be presented. Relations of our results to the multigrid convergence theory will be discussed. In combination with a self-adaptive smoothing strategy efficient multigrid solvers can be constructed. |
| Beschreibung: | 23 S. |
Internformat
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| 100 | 1 | |a Rüde, Ulrich |d 1957- |e Verfasser |0 (DE-588)111660041 |4 aut | |
| 245 | 1 | 0 | |a Local corrections for eliminating the pollution effect of reentrant corners |
| 264 | 1 | |a München |c 1989 | |
| 300 | |a 23 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Technische Universität <München>: TUM |v 8901 | |
| 520 | 3 | |a Abstract: "The accurate numerical solution of elliptic partial differential equations with singular solutions is particularly difficult: The error increases all over the solution domain by the so-called pollution effect. This paper examines local corrections, where only few of the discrete equations must be modified, independent of the meshsize. Using these modifications, the pollution effect can be suppressed, so that [formula] accuracy can be obtained by linear finite elements. The proof is based on the variation formulation and will be outlined for the case of Poisson's equation with reentrant corners. This generalizes previous results based on finite difference approximations on equidistant grids | |
| 520 | 3 | |a Applications of this correction technique within the multigrid method will be presented. Relations of our results to the multigrid convergence theory will be discussed. In combination with a self-adaptive smoothing strategy efficient multigrid solvers can be constructed. | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Poisson algebras | |
| 830 | 0 | |a Technische Universität <München>: TUM |v 8901 |w (DE-604)BV006185376 |9 8901 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006160297 | ||
Datensatz im Suchindex
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| author | Rüde, Ulrich 1957- |
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| author_sort | Rüde, Ulrich 1957- |
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| id | DE-604.BV009258237 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:34:01Z |
| institution | BVB |
| language | English |
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| physical | 23 S. |
| publishDate | 1989 |
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| series | Technische Universität <München>: TUM |
| series2 | Technische Universität <München>: TUM |
| spelling | Rüde, Ulrich 1957- Verfasser (DE-588)111660041 aut Local corrections for eliminating the pollution effect of reentrant corners München 1989 23 S. txt rdacontent n rdamedia nc rdacarrier Technische Universität <München>: TUM 8901 Abstract: "The accurate numerical solution of elliptic partial differential equations with singular solutions is particularly difficult: The error increases all over the solution domain by the so-called pollution effect. This paper examines local corrections, where only few of the discrete equations must be modified, independent of the meshsize. Using these modifications, the pollution effect can be suppressed, so that [formula] accuracy can be obtained by linear finite elements. The proof is based on the variation formulation and will be outlined for the case of Poisson's equation with reentrant corners. This generalizes previous results based on finite difference approximations on equidistant grids Applications of this correction technique within the multigrid method will be presented. Relations of our results to the multigrid convergence theory will be discussed. In combination with a self-adaptive smoothing strategy efficient multigrid solvers can be constructed. Differential equations Poisson algebras Technische Universität <München>: TUM 8901 (DE-604)BV006185376 8901 |
| spellingShingle | Rüde, Ulrich 1957- Local corrections for eliminating the pollution effect of reentrant corners Technische Universität <München>: TUM Differential equations Poisson algebras |
| title | Local corrections for eliminating the pollution effect of reentrant corners |
| title_auth | Local corrections for eliminating the pollution effect of reentrant corners |
| title_exact_search | Local corrections for eliminating the pollution effect of reentrant corners |
| title_full | Local corrections for eliminating the pollution effect of reentrant corners |
| title_fullStr | Local corrections for eliminating the pollution effect of reentrant corners |
| title_full_unstemmed | Local corrections for eliminating the pollution effect of reentrant corners |
| title_short | Local corrections for eliminating the pollution effect of reentrant corners |
| title_sort | local corrections for eliminating the pollution effect of reentrant corners |
| topic | Differential equations Poisson algebras |
| topic_facet | Differential equations Poisson algebras |
| volume_link | (DE-604)BV006185376 |
| work_keys_str_mv | AT rudeulrich localcorrectionsforeliminatingthepollutioneffectofreentrantcorners |