JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
Articles
Error analysis of the H1 gradient method for shape-optimization problems of continua
Daisuke MuraiHideyuki Azegami
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2013 Volume 5 Pages 29-32

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Abstract

We present an error estimation for the H1 gradient method, which provides numerical solutions to the shape-optimization problem of the domain in which a boundary value problem is defined. The main result is that if second-order elements are used for the solutions of the main and adjoint boundary value problems to evaluate the shape derivative, and the first-order elements are used for the solution of domain variation in the boundary value problem of the H1 gradient method, then we obtain first-order convergence of the solution of the domain variation with respect to the size of the finite elements.

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© 2013 The Japan Society for Industrial and Applied Mathematics
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