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 the L(infinity) norm are obtained. The results of numerical experiments which confirm the theoretical convergence rate are presented.
topological derivative shape optimization levelset method variational inequality asymptotic analysis