Locally different models in a checkerboard pattern with mesh adaptation and error control for multiple quantities of interest
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916264729903104 |
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| author | Endtmayer, Bernhard |
| author_facet | Endtmayer, Bernhard |
| contents | In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive partial differential equations in a checkerboard pattern, where the solution is continuous across the interface. In addition to the error estimation, the error can be localized using a partition of unity technique. The resulting adaptive algorithm is substantiated with a numerical example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locally different models in a checkerboard pattern with mesh adaptation and error control for multiple quantities of interest Endtmayer, Bernhard Numerical Analysis In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive partial differential equations in a checkerboard pattern, where the solution is continuous across the interface. In addition to the error estimation, the error can be localized using a partition of unity technique. The resulting adaptive algorithm is substantiated with a numerical example. |
| title | Locally different models in a checkerboard pattern with mesh adaptation and error control for multiple quantities of interest |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.18567 |