Pester, Cornelia

A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex Singularities

This thesis is concerned with the finite elementanalysis and the a posteriori error estimation foreigenvalue problems for general operator pencils on two-dimensional manifolds.A specific application of the presented theory is the computation of corner singularities.Engineers use the knowledge of the so-called singularity exponents to predict the onset and the propagation of cracks.All results of this thesis are explained for two model problems, the Laplace and the linear elasticity problem, and verified by numerous numerical results.