A PRIORI ERROR ESTIMATES FOR FINITE ELEMENT DISCRETIZATIONS OF A SHAPE OPTIMIZATION PROBLEM

被引：15

作者：

Kiniger, Bernhard ^{[1
]}

Vexler, Boris ^{[1
]}

机构：

[1] Tech Univ Munich, Fak Math, Lehrstuhl Optimale Steuerung, D-85748 Garching, Germany

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2013年 / 47卷 / 06期

基金：

奥地利科学基金会;

关键词：

Shape optimization; existence and convergence of approximate solutions; error estimates; finite elements; LIPSCHITZ-DOMAINS; ELLIPTIC-EQUATIONS; DESIGN-PROBLEMS; APPROXIMATION;

D O I：

10.1051/m2an/2013086

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider a model shape optimization problem. The state variable solves an elliptic equation on a domain with one part of the boundary described as the graph of a control function. We prove higher regularity of the control and develop a priori error analysis for the finite element discretization of the shape optimization problem under consideration. The derived a priori error estimates are illustrated on two numerical examples.

引用

页码：1733 / 1763

页数：31