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A Note on the Constants in Inverse Trace Inequalities for Polynomials Orthogonal to Lower-Order Subspaces
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DOI：10.1007/s10915-026-03422-5.png)
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Abstract
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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 $$\mathbb {P}_n(T)$$ , $$n\leqslant p$$ , 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]. 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.
Keywords:
hp-analysis
Inverse estimate
Discrete trace inequality
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3.3
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652
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9.6K
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