Topological Derivatives for Semilinear Elliptic Equations
Mohamed Iguernane, С. А. Назаров, Jean-Rodolphe Roche, Jan Sokołowski, Katarzyna Szulc · International Journal of Applied Mathematics and Computer Science · 2009
Topological Derivatives for Semilinear Elliptic Equations 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 theL∞norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.