DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS-Reference-Cited by-同舟云学术

DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS

Published:2002-05 Issue:05 Volume:12 Page:689-719
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

BABUŠKA IVO¹,GUO BENQI²

Affiliation:

1. Texas Institute for Computational and Applied Mathematics, University of Texas, Austin, TX 78712, USA

2. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada

Abstract

This is the second 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 weighted Besov spaces. In this paper, we combine the approximability of singular solutions in the Jacobi-weighted Besov spaces, which were analyzed in the previous paper,4 with the technique of partition of unity in order to prove the optimal rate of convergence of the p-version of the finite element method for elliptic boundary value problems on polygonal domains.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202502001854

Reference13 articles.

1. Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order

2. The $h{\text{ - }}p$ Version of the Finite Element Method for Domains with Curved Boundaries

3. The Optimal Convergence Rate of the p-Version of the Finite Element Method

4. The $h-p$ version of the finite element method with quasiuniform meshes

Cited by 33 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Theorems on direct and inverse approximation by algebraic polynomials and piecewise polynomials in the spaces Hm(a, b) and Bs2,q(a, b);Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika;2024-02-12

2. Theorems on Direct and Inverse Approximation by Algebraic Polynomials and Piecewise Polynomials in the Spaces $${{H}^{m}}(a,b)$$ and $$B_{{2,q}}^{s}(a,b)$$;Russian Mathematics;2024-01

3. Pointwise error estimates and local superconvergence of Jacobi expansions;Mathematics of Computation;2023-03-21

4. On Best Error Bounds for Approximations by Algebraic Polynomials and Splines in the Spaces $$\boldsymbol{W_{p}^{m}(a,b)}$$ and $$\boldsymbol{B_{p,q}^{s}(a,b)}$$;Lobachevskii Journal of Mathematics;2022-11

5. Direct and Inverse Theorems of the Approximation of Functions by Algebraic Polynomials and Splines in the Norms of the Sobolev Space;Russian Mathematics;2022-06