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Polynomial extensions play a vital role in the analysis of the pand h-pFEM 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)...
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