On the finite element method for the biharmonic dirichlet problem in polygonal domains; quasi-optimal rate of convergence

2005 ◽  
Vol 22 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Akira Mizutani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dirichlet Problem ◽  
Rate Of Convergence ◽  
Optimal Rate ◽  
The Finite Element Method ◽  
Polygonal Domains ◽  
Optimal Rate Of Convergence ◽  
Element Method ◽  
Biharmonic Dirichlet Problem

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

2002 ◽  
Vol 12 (05) ◽  
pp. 689-719 ◽  
Author(s):  
IVO BABUŠKA ◽  
BENQI GUO
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rate Of Convergence ◽  
Besov Spaces ◽  
The Finite Element Method ◽  
Optimal Rate Of Convergence ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Weighted Besov Spaces ◽  
Element Method

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.

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