19th April – ‪Christos Xenophontos: Finite Element approximation of singularly perturbed eigenvalue problems

We consider singularly perturbed eigenvalue problems in one-dimension, and their numerical approximation by the (standard Galerkin) Finite Element Method (FEM). These are fourth order equations, where a small parameter multiplies the highest order derivative. We will present results for an $h$ version FEM with polynomials of degree $p$ on an exponentially graded (eXp) mesh, as well as an $hp$ version FEM on the so-called Spectral Boundary Layer (SBL) mesh. For both methods, robust optimal convergence is shown for the eigenvalues and associated eigenfunctions. Numerical results, illustrating the theory, will also be presented.