scholarly journals Two Algorithms for a Class of Elliptic Problems in Shape Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Li Tian ◽  
Dai Xiaoxia ◽  
Zhang Chengwei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Design ◽  
Shape Optimization ◽  
Variational Problem ◽  
Optimization Problem ◽  
Elliptic Boundary ◽  
The Finite Element Method ◽  
Numerical Examples ◽  
Elliptic Boundary Value

We propose two algorithms for elliptic boundary value problems in shape optimization. With the finite element method, the optimization problem is replaced by a discrete variational problem. We give rules and use them to decide which elements are to be reserved. Those rules are determined by the optimization; as a result, we get the optimal design in shape. Numerical examples are provided to show the effectiveness of our algorithms.

Convergence Analysis for the Elliptic Boundary Value Problem of Rectangle Nested Refinement Finite Element with Q1 Truncation

2012 ◽  
Vol 182-183 ◽  
pp. 1567-1570
Author(s):  
Qi Sheng Wang ◽  
Yi Gao Zhao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Elliptic Equation ◽  
Elliptic Boundary ◽  
Grid Refinement ◽  
Elliptic Boundary Value Problem ◽  
The Finite Element Method ◽  
Boundary Problems ◽  
Elliptic Boundary Value ◽  
Affine Mappings

In this paper, the finite element method of rectangle nested refinement was introduced, and the level Κ rectangle grid refinement and related properties on planar region were given. According to boundary problems of a kind of elliptic equation, the results of the convergence were proved for the finite element of Κ level rectangle nested refinement under Q1mappings by affine mappings replaced.

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