International Journal of applied mathematics and computer science

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Paper details

Number 2 - June 2009
Volume 19 - 2009

Topological derivatives for semilinear elliptic equations

Mohamed Iguernane, Serguei A. Nazarov, Jean-Rodolphe Roche, Jan Sokolowski, Katarzyna Szulc

The form of topological derivatives for an integral shape functional is derived for a class of semilinear elliptic equations. The convergence of finite element approximation for the topological derivatives is shown and the error estimates in the L norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.

shape optimization, topological derivative, levelset method, variational inequality, asymptotic analysis