scholarly journals High-order local rate of convergence by mesh-refinement in the finite element method

1985 ◽  
Vol 45 (171) ◽  
pp. 109-109 ◽  
Author(s):  
Kenneth Eriksson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rate Of Convergence ◽  
Mesh Refinement ◽  
High Order ◽  
The Finite Element Method ◽  
Local Rate ◽  
Element Method

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.

Reduction of stress concentration around a hole in a uniaxially loaded plate

1983 ◽  
Vol 18 (2) ◽  
pp. 135-141 ◽  
Author(s):  
U C Jindal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Circular Hole ◽  
High Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Loaded Plate ◽  
Hole Geometry ◽  
Element Method

The stress concentration around a circular hole in a plate can be reduced by up to 21 per cent by introducing auxiliary holes on either side of the original hole. But this approach of auxiliary holes creates two more regions of stress concentration in the plate. In the present study, the hole geometry has been modified to effect stress reductions as high as 22 per cent. The problem has been analysed numerically by the finite element method and experimentally by two-dimensional photoelasticity. It has been observed that by making the hole oblong in the direction of loading, a high order of reduction in stress concentration around the hole can be obtained.

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