Stable Lifting of Polynomial Traces on Triangles

Abstract

We construct a right inverse of the trace operator $u\mapsto (u{|}_{\partial T},{\partial }_{n}u{|}_{\partial T})$ on the reference triangle $T$ that maps suitable piecewise polynomial data on $\partial T$ into polynomials of the same degree and is bounded in all $W^{s,q}(T)$ norms with $1<q<\infty$ and $s\ge 2$. The analysis relies on new stability estimates for three classes of single edge operators. We then generalize the construction for $m$th-order normal derivatives, $m\in {\mathbb{N}}_0$.

27 pages, 1 figure