Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910480567631872 |
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| author | Bartels, Sören Kaltenbach, Alex |
| author_facet | Bartels, Sören Kaltenbach, Alex |
| contents | A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems, problems involving jumping coefficients, and finite element methods using anisotropic triangulations, such estimates often involve large factors, leading to sub-optimal error estimates. By making use of convex duality arguments, exact and explicit error representations are derived that avoid such effects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction Bartels, Sören Kaltenbach, Alex Numerical Analysis 35Q68, 49M25, 49M29, 65K15, 65N15, 65N50 A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems, problems involving jumping coefficients, and finite element methods using anisotropic triangulations, such estimates often involve large factors, leading to sub-optimal error estimates. By making use of convex duality arguments, exact and explicit error representations are derived that avoid such effects. |
| title | Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction |
| topic | Numerical Analysis 35Q68, 49M25, 49M29, 65K15, 65N15, 65N50 |
| url | https://arxiv.org/abs/2402.06429 |