Higher order meshless schemes applied to the finite element method in elliptic problems

2019 ◽  
Vol 77 (3) ◽  
pp. 779-802
Author(s):  
Sławomir Milewski ◽  
Roman Putanowicz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elliptic Problems ◽  
Higher Order ◽  
The Finite Element Method ◽  
Element Method

Application of the Williams Expansion near a Bi-Material Interface

2017 ◽  
Vol 754 ◽  
pp. 206-209 ◽  
Author(s):  
Lucie Malíková ◽  
Stanislav Seitl
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Crack Tip ◽  
Higher Order ◽  
Simplified Model ◽  
The Finite Element Method ◽  
Material Interface ◽  
Higher Order Terms ◽  
Element Method ◽  
Crack Tip Stress

A simplified model of a crack approaching a bi-material interface is modelled by means of the finite element method in order to investigate the significance of the higher-order terms of the Williams expansion for the proper approximation of the opening crack-tip stress near the bi-material interface. The discussion on results is presented and the importance of the higher-order terms proved.

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.

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