Old and new results on the finite element approximation of Maxwell eigenvalues

Daniele Boffi

Sept. 16, 2003, 2 p.m. T 857

The analysis on the finite element approximation of Maxwell eigenvalues (based on the construction of a Fortin operator with suitable properties in order to guarantee the discrete compactness) shows that the use of edge finite elements is the natural choice to face the problem under consideration. In this talk we recall the basic theory of eigenvalue approximation, including the approximation of eigenvalues in mixed form. Then we recall how the theory can be applied to the approximation of Maxwell eigenvalues. Then, we present more recent results, showing how the previous analysis extents to the simulation of photonic crystals and, finally, we address the issue of the use of general quadrilateral meshes and we describe a new finite element families on quadrilaterals which satisfies the discrete compactness property.