Best approximation for the 𝑝-version of the finite element method in three dimensions in the framework of the Jacobi-weighted Besov spaces

2003 ◽  
pp. 139-156 ◽  
Author(s):  
Benqi Guo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Besov Spaces ◽  
Best Approximation ◽  
Three Dimensions ◽  
The Finite Element Method ◽  
Weighted Besov Spaces ◽  
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.

New Development of the P and H-P Version Finite Element Method with Quasi-Uniform Meshes for Elliptic Problems

2013 ◽  
Vol 444-445 ◽  
pp. 671-675
Author(s):  
Jian Ming Zhang ◽  
Yong He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Automobile Industry ◽  
Large Scale ◽  
Elliptic Problems ◽  
Three Dimensions ◽  
The Finite Element Method ◽  
New Development ◽  
Engineering Problems ◽  
Element Method

In recent three decades, the finite element method (FEM) has rapidly developed as an important numerical method and used widely to solve large-scale scientific and engineering problems. In the fields of structural mechanics such as civil engineering , automobile industry and aerospace industry, the finite element method has successfully solved many engineering practical problems, and it has penetrated almost every field of today's sciences and engineering, such as material science, electricmagnetic fields, fluid dynamics, biology, etc. In this paper, we will overview and summarize the development of the p and h-p version finite element method, and introduce some recent new development and our newest research results of the p and h-p version finite element method with quasi-uniform meshes in three dimensions for elliptic problems.

Structure Analysis with 3D Hexahedral Meshes Generated by a Label-Driven Subdivision

2018 ◽  
Vol 12 (1) ◽  
pp. 113-122
Author(s):  
Bo Liu ◽  
◽  
Kenjiro T. Miura ◽  
Shin Usuki
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structure Analysis ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Hexahedral Element ◽  
Hexahedral Meshes ◽  
Subdivision Algorithm ◽  
Element Method

For structure analysis with the finite element method (FEM), the hexahedral element is preferable to the tetrahedral one from the viewpoint of accuracy. Previously, we had introduced a label-driven subdivision method for a two-dimensional mesh and showed that the meshes generated by our method were useful for structural analyses. In this study, we extend our two-dimensional algorithm to three-dimensions and verify that the meshes generated by the proposed mesh-subdivision algorithm are useful for structural analyses.

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