Finite Element Approximation of Eigenvalue Problems

In this course we will introduce the students to the numerical analysis of eigenvalue problems associated with partial differential equations. Starting from easy numerical toy problems, we will show that in the case of standard elliptic equations any numerical scheme working well for the source problem can be applied successfully to the corresponding eigenvalue problem. This is not the case when eigenvalue problems in mixed form are considered. In this situation the classic inf-sup conditions are neither sufficient nor necessary for the correct approximation of the spectrum. We will describe the differences with examples and counterexamples.

• Advanced