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

被引：85

作者：

Babuska, I ^{[1
]}

Guo, BQ

机构：

[1] Univ Texas, Texas Inst Computat & Appl Math, Austin, TX 78712 USA

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2002年 / 39卷 / 05期

关键词：

Jacobi-weighted Besov spaces; modified Jacobi-weighted Besov spaces; Jacobi weights; singular function of r(gamma)-type and r(gamma) log(upsilon) r-type; approximability; the p-version of the finite element method;

D O I：

10.1137/S0036142901356551

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is the first of a series devoted to the approximation theory of the p-version of the finite element method in two dimensions in the framework of the Jacobi-weighted Besov spaces, which provides the p-version with a solid mathematical foundation. In this paper, we establish a mathematical framework of the Jacobi-weighted Besov and Sobolev spaces and analyze the approximability of the functions in the framework of these spaces, particularly, singular functions of r(gamma)-type and r(gamma) log(nu) r-type. These spaces and the corresponding approximation properties are of fundamental importance to the proof of the optimal convergence for the p-version in two dimensions in part II and to various sharp inverse approximation theorems in part III.

引用

页码：1512 / 1538

页数：27