Stable lifting of polynomial traces on triangles - Parker, C; Suli, E (Society for Industrial and Applied Mathematics, 2024)
We construct a right inverse of the trace operator u 7→ (u|∂T , ∂nu|∂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 Ws,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 ∈ N0.