Stable Liftings of Polynomial Traces on Tetrahedra

2024/02/24 by Parker, Charles, Süli, Endre · 1 citation
#46E35 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2402.15789

Abstract

On the reference tetrahedron K, we construct, for each k ∈ ℕ₀, a right inverse for the trace operator u ↦ (u, ∂_n u, …, ∂_n^k u)|_{∂ K}. The operator is stable as a mapping from the trace space of W^{s, p}(K) to W^{s, p}(K) for all p ∈ (1, ∞) and s ∈ (k+1/p, ∞). Moreover, if the data is the trace of a polynomial of degree N ∈ ℕ₀, then the resulting lifting is a polynomial of degree N. One consequence of the analysis is a novel characterization for the range of the trace operator.

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