Stable Lifting of Polynomial Traces on Triangles

04/25/2023

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by   Charles Parker, et al.

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We construct a right inverse of the trace operator u ↦ (u|_∂ T, ∂_n u|_∂ T) on the reference triangle T that maps suitable piecewise polynomial data on ∂ T into polynomials of the same degree and is bounded in all W^s, q(T) norms with 1 < q <∞ and s ≥ 2. The analysis relies on new stability estimates for three classes of single edge operators. We then generalize the construction for mth-order normal derivatives, m ∈ℕ_0.