On the constants in inverse trace inequalities for polynomials orthogonal to lower-order subspaces
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| Format: | Preprint |
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2025
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| _version_ | 1866918250426662912 |
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| author | Dong, Zhaonan Wadhawan, Tanvi |
| author_facet | Dong, Zhaonan Wadhawan, Tanvi |
| contents | We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to $\mathbb{P}_p(T)$ (polynomial space with total degree $p$) that are orthogonal to the lower-order subspace $\mathbb{P}_n(T)$, $n\leq p$, where $T$ denotes a $d$-dimensional simplex. The proofs rely on orthogonal polynomial expansions on reference simplices and on a careful analysis of the eigenvalues of the relevant blocks of the face mass matrices, following the arguments developed in [9]. These results are very useful in the $hp$-analysis of the hybrid Galerkin methods, e.g. hybridizable discontinuous Galerkin methods, hybrid high-order methods, etc. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the constants in inverse trace inequalities for polynomials orthogonal to lower-order subspaces Dong, Zhaonan Wadhawan, Tanvi Numerical Analysis 65N30 We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to $\mathbb{P}_p(T)$ (polynomial space with total degree $p$) that are orthogonal to the lower-order subspace $\mathbb{P}_n(T)$, $n\leq p$, where $T$ denotes a $d$-dimensional simplex. The proofs rely on orthogonal polynomial expansions on reference simplices and on a careful analysis of the eigenvalues of the relevant blocks of the face mass matrices, following the arguments developed in [9]. These results are very useful in the $hp$-analysis of the hybrid Galerkin methods, e.g. hybridizable discontinuous Galerkin methods, hybrid high-order methods, etc. |
| title | On the constants in inverse trace inequalities for polynomials orthogonal to lower-order subspaces |
| topic | Numerical Analysis 65N30 |
| url | https://arxiv.org/abs/2512.14570 |