Abstract
This talk is devoted to the finite element approximation of boundary value problems with interfaces. We shall consider a simple second order elliptic equation with discontinuous coefficients and present the most common approaches for its finite element discretization. One main feature of these methods consists in the construction of the mesh which can be /fitted/ or /unfitted/. In the first case the mesh is constructed such that the elements are not cut by the interface, so that the resulting approximation has optimal rate of convergence according to the regularity of the solution. Unfitted meshes are independent of the position of the interface, leading possibly to non optimal rate of convergence of the approximation. In particular, we shall present methods based on the introduction of a Lagrange multiplier and to penalization techniques to enforce weakly the transmission conditions across the interface. These approaches can be efficiently extended to the finite element approximation of fluid-structure interaction systems and we shall discuss in particular the fictitious domain approach that we developed in several papers.
Brief Biography
Lucia Gastaldi is a Professor of Numerical Analysis in Dipartimento di Ingegneria Civile, Architettura, Territorio, Ambiente e di Matematica at Universita degli Studi di Brescia. She earned her Lauream Degree in Mathematics at Universita degli Studi di Pavia in 1978. Her scientific interest regards the approximation by finite elements of partial differential equations. In particular, she is interested in error estimates for mixed and nonconforming finite elements, finite element discretization of eigenvalue problems, fluid-structure interaction problems, and adaptive finite element methods.