Approximation of a simply supported plate with obstacle

We discuss an algorithm for the solution of variational inequalities associated to simply supported plates in contact with a rigid obstacle. Our approach has a fixed domain character, uses just linear equations and approximates both the solution and the corresponding coincidence set. Numerical examples are also provided

Extension theorems related to a fluid-structure interaction problem

The aim of this paper is to prove the existence of an approximate weak solution for a steady fluid-structure interaction problem. A fictitious domain approach with penalization is used. One of the main ingredients is an extension theorem for domains with Lipschitz boundaries. The fluid and structure domains are not necessarily double connected and the structure is not completely surrounded by the fluid. These assumptions are more realistic for some engineering and medical applications