Christos Xenophontos Tuesday 19th April at 14:00
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.
This is joint work with H. G. Roos.