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

Authors:
Benqi Guo;Weiwei Sun
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 4

Superconvergence of the h-p version of the finite element method in one dimension

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

SIAM Journal on Numerical Analysis
Full length article: Direct and inverse approximation theorems for the p-version of the finite element method in the framework of weighted Besov spaces, part III: Inverse approximation theorems

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

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Abstract

In the framework of the Jacobi-weighted Besov spaces, we analyze the convergence of the $h$-$p$ version of finite element solutions on quasi-uniform meshes and the lower and upper bounds of errors for elliptic problems on polygons. Both lower and upper bounds are proved to be optimal in $h$ and $p$, which leads to the optimal convergence of the $h$-$p$ version of the finite element method with quasi-uniform meshes for elliptic problems on polygons. The results proved for the $h$-$p$ version include the $h$-version with quasi-uniform meshes and the $p$-version with quasi-uniform degrees as two special cases.