Optimal Control Problems in Nonsmooth Solid and Fluid Mechanics : Computational Aspects

Abstract

The paper is devoted to numerical realization of nonsmooth optimal control problems in solid and fluid mechanics with special emphasis on contact shape optimization and parameter identification in fluid flow models. Nonsmoothness is usually owing to the state constraint, typically given by an inequality type problem governing the optimized system. To remove the nonsmooth character, which complicates numerical realization, the penalization/regularization of the state constraint is used. The resulting optimal control problem becomes smooth and it can be solved by standard methods of smooth optimization. This approach is illustrated with a parameter identification in the system driven by the Stokes equation with threshold slip boundary conditions.