2025/12/16 by Zhaonan Dong, Tanvi Wadhawan, Dong, Zhaonan +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Mathematical functions and polynomials #Matrix Theory and Algorithms #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2512.14570
openalex publication_date 2025/12/16 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28
We derive sharp, explicit constants in inverse trace inequalities for polynomial functions belonging to ℙp(T) (polynomial space with total degree p) that are orthogonal to the lower-order subspace ℙn(T), n≤ 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~\citewarburton2003constants. The novelty is that the extremal face-mass eigenvalue is computed after removing the polynomial modes of degree at most n. This yields inverse trace inequality constants involving the factor (p-n)(p+n+d+1) instead of the classical factor (p+1)(p+d), and therefore quantifies the gain in p available in projection-error estimates. 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.