A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908777726345216 |
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| author | Chaumont-Frelet, T. |
| author_facet | Chaumont-Frelet, T. |
| contents | We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to prove efficiency estimates without extra stabilization terms in the error measure for a large class of discretization schemes. We propose a residual-based estimator for which the efficiency constant scales optimally in polynomial degree, as well as two equilibrated estimators that are polynomial-degree-robust. One of the two estimators further leads to asymptotically constant-free error bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds Chaumont-Frelet, T. Numerical Analysis We propose new a posteriori error estimators for non-conforming finite element discretizations of second-order elliptic PDE problems. These estimators are based on novel reformulations of the standard Prager-Synge identity, and enable to prove efficiency estimates without extra stabilization terms in the error measure for a large class of discretization schemes. We propose a residual-based estimator for which the efficiency constant scales optimally in polynomial degree, as well as two equilibrated estimators that are polynomial-degree-robust. One of the two estimators further leads to asymptotically constant-free error bounds. |
| title | A new family of a posteriori error estimates for non-conforming finite element methods leading to stabilization-free error bounds |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2506.23381 |