Error analysis for a Crouzeix-Raviart approximation of the obstacle problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913718071197696 |
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| author | Bartels, Sören Kaltenbach, Alex |
| author_facet | Bartels, Sören Kaltenbach, Alex |
| contents | In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. Numerical experiments are carried out to support the theoretical findings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01646 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Error analysis for a Crouzeix-Raviart approximation of the obstacle problem Bartels, Sören Kaltenbach, Alex Numerical Analysis 35J20, 49J40, 49M29, 65N30, 65N15, 65N50 In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements of a triangulation. We establish a priori error estimates imposing natural regularity assumptions, which are optimal, and the reliability and efficiency of a primal-dual type a posteriori error estimator for general obstacles and involving data oscillation terms stemming only from the right-hand side. Numerical experiments are carried out to support the theoretical findings. |
| title | Error analysis for a Crouzeix-Raviart approximation of the obstacle problem |
| topic | Numerical Analysis 35J20, 49J40, 49M29, 65N30, 65N15, 65N50 |
| url | https://arxiv.org/abs/2302.01646 |