Reprint of “Construction of polynomial extensions in two dimensions and application to the h-p finite element method”

摘要

Polynomial extensions play a vital role in the analysis of the p and h-p FEM as well as the spectral element method. In this paper, we construct explicitly polynomial extensions on a triangle T and a square S, which lift a polynomial defined on a side Γ or on whole boundary of T or S. The continuity of these extension operators from H0012(Γ) to H1(T) or H1(S) and from H12(∂T) to H1(T) or from H12(∂S) to H1(S) is rigorously proved in a constructive way. Applications of these polynomial extensions to the error analysis for the h-p FEM are presented.