Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910475731599360 |
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| author | Kaltenbach, Alex |
| author_facet | Kaltenbach, Alex |
| contents | In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,δ)$-structure for some $p\in (1,\infty)$ and $δ\ge 0$. We establish a priori error estimates, which are optimal for all $p\in (1,\infty)$ and $δ\ge 0$, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12116 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem Kaltenbach, Alex Numerical Analysis 49M29, 65N15, 65N50 In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,δ)$-structure for some $p\in (1,\infty)$ and $δ\ge 0$. We establish a priori error estimates, which are optimal for all $p\in (1,\infty)$ and $δ\ge 0$, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments. |
| title | Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem |
| topic | Numerical Analysis 49M29, 65N15, 65N50 |
| url | https://arxiv.org/abs/2210.12116 |