Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910233700335616 |
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| author | Chaumont-Frelet, T. |
| author_facet | Chaumont-Frelet, T. |
| contents | We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori error estimation purposes. Our numerical lower bound is based on two discrete singular value problems involving a Lagrange finite element discretization coupled with an a posteriori error estimator based on flux reconstruction techniques. We show that if the finite element discretization is sufficiently rich, our lower bound underestimates the optimal constant only by a factor roughly equal to two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00404 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality Chaumont-Frelet, T. Numerical Analysis We propose an algorithm to numerically determined whether a second-order linear PDE problem satisfying a Garding inequality is well-posed. This algorithm further provides a lower bound to the inf-sup constant of the weak formulation, which may in turn be used for a posteriori error estimation purposes. Our numerical lower bound is based on two discrete singular value problems involving a Lagrange finite element discretization coupled with an a posteriori error estimator based on flux reconstruction techniques. We show that if the finite element discretization is sufficiently rich, our lower bound underestimates the optimal constant only by a factor roughly equal to two. |
| title | Guaranteed stability bounds for second-order PDE problems satisfying a Garding inequality |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2601.00404 |