Topological derivatives for semilinear elliptic equations - Iguernane, Mohamed; Nazarov, Serguei A.; Roche, Jean-Rodolphe; Sokołowski, Jan; Szulc, Katarzyna (Zielona Góra: Uniwersytet Zielonogórski)
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.
Keywords: shape optimization; topological derivative; levelset method; variational inequality; asymptotic analysis