Constructive Method for Polynomial Extensions in Two Dimensions

Polynomial extensions play a vital role in numerical analysis of some high-order approximation, such as the p version and the h-p version of the finite element method and spectral methods. In this paper, we construct explicitly polynomial extensions on a triangleTand a squareS, which lift a polynomial defined on a side Γor on whole boundary of TorS. These extension operators from1/200()HΓ to1()HTor 1()HSand from1/2()HT∂to1()HTor from1/2()HS∂ to1()HSare continuous.