학술논문
The Optimal Convergence of the h-p Version of the Finite Element Method with Quasi-Uniform Meshes
Document Type
research-article
Author
Source
SIAM Journal on Numerical Analysis, 2007 Jan 01. 45(2), 698-730.
Subject
Language
English
ISSN
00361429
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.