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

Authors:
Benqi Guo;Ivo BabušKa
Affiliations:
-;-
Venue:
Journal of Approximation Theory
Year:
2013

Citing 13
Cited 0

The approximation of solutions of elliptic boundary-value problems via the p-version of the finite element method

SIAM Journal on Numerical Analysis
Regularity of the solution of elliptic problems with piecewise analytic data. Part 1. Boundary value problems for linear elliptic equation of second order

SIAM Journal on Mathematical Analysis
Efficient preconditioning for the p-version finite element method in two dimensions

SIAM Journal on Numerical Analysis
On the L2 error for the p-version of the finite element method over polygonal domains

Computer Methods in Applied Mechanics and Engineering
The P and H-P versions of the finite element method, basic principles and properties

SIAM Review
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

SIAM Journal on Numerical Analysis
Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

Journal of Approximation Theory
The optimal rate of convergence of the p-version of the boundary element method in two dimensions

Numerische Mathematik
Approximation Theory for the p-Version of the Finite Element Method in Three Dimensions. Part 1: Approximabilities of Singular Functions in the Framework of the Jacobi-Weighted Besov and Sobolev Spaces

SIAM Journal on Numerical Analysis
The Optimal Convergence of the $h$-$p$ Version of the Finite Element Method with Quasi-Uniform Meshes

SIAM Journal on Numerical Analysis
Generalized Jacobi polynomials/functions and their applications

Applied Numerical Mathematics
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

SIAM Journal on Numerical Analysis
Local Jacobi Operators and Applications to the $p$-Version of Finite Element Method in Two Dimensions

SIAM Journal on Numerical Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

This is the third of a series devoted to the direct and inverse approximation theorems of the p-version of the finite element method in the framework of the Jacobi-weighted Besov and Sobolev spaces. In this paper we derive the inverse algebraic approximation in terms of the Jacobi-weighted Besov spaces and prove the inverse theorems for the finite element solutions of the p-version in the Chebyshev-weighted Besov spaces based upon the convergence rate measured in the energy norms.