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

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 Gamma or on whole boundary of T or S. The continuity of these extension operators from H-00(1/2)(F) to H-1(T) or H-1(S) and from H-1/2 (partial derivative T) to H-1(T) or from H-1/2 (partial derivative S) to H-1(S) is rigorously proved in a constructive way. Applications of these polynomial extensions to the error analysis for the h-p FEM are presented. (C) 2013 Elsevier B.V. All rights reserved.