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Topological derivatives for semilinear elliptic equations

Mohamed Iguernane;  Serguei A. Nazarov;  Jean-Rodolphe Roche;  Jan Sokolowski;  Katarzyna Szulc — 2009

International Journal of Applied Mathematics and Computer Science

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.

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