Topological derivatives for semilinear elliptic equations

Mohamed Iguernane (1) , Sergueï A. Nazarov (2) , Jean Rodolphe Roche (3) , Jan Sokolowski (1) , Katarzyna Szulc (1)

1 IECN - Institut Élie Cartan de Nancy
2 IPME - Institute of Mechanical Engineering Problems [St. Petersburg]
3 CALVI - Scientific computation and visualization

The form of topological derivatives for 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 $L^{\infty}$ norm are obtained. Results of numerical experiments which confirm the theoretical convergence rate are presented.

Mots clés: Shape optimization; topological derivative; levelset method; variational inequality; asymptotic analysis

Domaines: Equations aux dérivées partielles [math.AP]

Mohamed Iguernane, Sergueï A. Nazarov, Jean Rodolphe Roche, Jan Sokolowski, Katarzyna Szulc. Topological derivatives for semilinear elliptic equations. International Journal of Applied Mathematics and Computer Science, 2009, 19 (2), pp.191-205. ⟨10.2478/v10006-009-0016-4⟩. ⟨hal-00318584⟩