ON FINITE ELEMENT APPROXIMATIONS TO A SHAPE GRADIENT FLOW IN SHAPE OPTIMIZATION OF ELLIPTIC PROBLEMS  

作　　者：Chunxiao Liu Shengfeng Zhu 

机构地区：[1]School of Statistics and Mathematics,Shanghai Lixin University of Accounting and Finance,Shanghai 201209,China [2]Department of Mathematics&Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,East China Normal University,Shanghai 200241,China

出　　处：《Journal of Computational Mathematics》2023年第5期956-979,共24页计算数学（英文）

基　　金：supported in part by the National Key Basic Research Program under grant 2022YFA1004402;the Science and Technology Commission of Shanghai Municipality(Nos.21JC1402500,22ZR1421900,and 22DZ2229014);the National Natural Science Foundation of China under grant(No.12071149).

摘　　要：Shape gradient flows are widely used in numerical shape optimization algorithms.We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems.We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative.Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions.

关 键 词：Shape optimization Shape gradient Eulerian derivative Finite element Error estimate 

分 类 号：O241.82[理学—计算数学]