Topological Derivatives for Semilinear Elliptic Equations

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

doi:10.2478/v10006-009-0016-4

Abstract

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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Topological Derivatives for Semilinear Elliptic Equations

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