Abstract:
We discuss the finite element approximation of eigenvalue problems depending on one more more deterministic parameters. The parameters can be found in the description of the PDE or can be introduced by the numerical discretization. The regularity of the solutions, as well as the presence of crossing between eigenvalues, is an important issue that plays a crucial role for the design of efficient approximating schemes. Several examples are presented which describe the problem and propose some possible numerical approaches.

Bio:
Daniele Boffi is professor of applied mathematics from 2020 at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. Since this year he serves as Associate Dean of the CEMSE (Computer, Electrical and Mathematical Sciences and Engineering) Division. Before joining KAUST he was professor of numerical analysis at the University of Pavia in Italy. His research is devoted to the numerical approximation of partial differential equations, with particular interest in the finite element method and in mixed finite elements. Some of his most active research areas concern the approximation of eigenvalue problems arising from partial differential equations and the numerical modeling of fluid-structure interaction problems. He is coauthor of one of the most widely used book on mixed finite elements and he is author of a highly cited survey on the approximation of eigenvalue problems. During his academic career at the University of Pavia he has been involved in several administrative duties, including being member of the Academic Senate, Director of the PhD Higher Education School, and member of the Evaluation Committee.