Plain convergence of goal-oriented adaptive FEM
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Soggetti: | |
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| _version_ | 1866909270946086912 |
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| author | Helml, Valentin Innerberger, Michael Praetorius, Dirk |
| author_facet | Helml, Valentin Innerberger, Michael Praetorius, Dirk |
| contents | We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural properties of the error estimators, namely stability on non-refined elements as well as reduction on refined elements. In particular, the second setting does not require reliability and efficiency estimates. Numerical experiments underline our theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10143 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Plain convergence of goal-oriented adaptive FEM Helml, Valentin Innerberger, Michael Praetorius, Dirk Numerical Analysis We discuss goal-oriented adaptivity in the frame of conforming finite element methods and plain convergence of the related a posteriori error estimator for different general marking strategies. We present an abstract analysis for two different settings. First, we consider problems where a local discrete efficiency estimate holds. Second, we show plain convergence in a setting that relies only on structural properties of the error estimators, namely stability on non-refined elements as well as reduction on refined elements. In particular, the second setting does not require reliability and efficiency estimates. Numerical experiments underline our theoretical findings. |
| title | Plain convergence of goal-oriented adaptive FEM |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2208.10143 |