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

Authors:
Benqi Guo;Jianming Zhang
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 9
Cited 0

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The Schwarz algorithm for spectral methods

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Efficient preconditioning for the p-version finite element method in two dimensions

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Polynomial Liftings on a Tetrahedron and Applications to the h-p Version of the Finite Element Method in Three Dimensions

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Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces

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The Optimal Convergence of the $h$-$p$ Version of the Finite Element Method with Quasi-Uniform Meshes

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Stable and Compatible Polynomial Extensions in Three Dimensions and Applications to the $p$ and $h$-$p$ Finite Element Method

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Approximation Theory for the P-Version of the Finite Element Method in Three Dimensions Part II: Convergence of the $P$ Version of the Finite Element Method

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Local Jacobi Operators and Applications to the $p$-Version of Finite Element Method in Two Dimensions

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Abstract

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 @C or on whole boundary of T or S. The continuity of these extension operators from H"0"0^1^2(@C) to H^1(T) or H^1(S) and from H^1^2(@?T) to H^1(T) or from H^1^2(@?S) to H^1(S) is rigorously proved in a constructive way. Applications of these polynomial extensions to the error analysis for the h-pFEM are presented.