A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910438642417664 |
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| author | Porwal, Kamana Singla, Ritesh |
| author_facet | Porwal, Kamana Singla, Ritesh |
| contents | In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$ polynomials, where $r=0$ and $s$ is either $0$ or $1$. The discrete obstacle constraints are specifically applied to the cell unknowns. The analysis hinges on the construction of a suitable Lagrange multiplier, a residual functional and a linear averaging map. The reliability and the efficiency of the proposed a posteriori error estimator is discussed, and the study is concluded by numerical experiments supporting the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem Porwal, Kamana Singla, Ritesh Numerical Analysis In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$ polynomials, where $r=0$ and $s$ is either $0$ or $1$. The discrete obstacle constraints are specifically applied to the cell unknowns. The analysis hinges on the construction of a suitable Lagrange multiplier, a residual functional and a linear averaging map. The reliability and the efficiency of the proposed a posteriori error estimator is discussed, and the study is concluded by numerical experiments supporting the theoretical results. |
| title | A posteriori error analysis of hybrid higher order methods for the elliptic obstacle problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.04961 |