ubc A posteriori error estimation for non-linear eigenvalue problems for differential operators of second order with focus on 3D vertex singularities 2006-05-07 [Electronic ed.] prv Universitätsbibliothek Chemnitz Universitätsbibliothek Chemnitz, Chemnitz Fakultät für Mathematik female Karl-Marx-Stadt male male male This thesis is concerned with the finite element analysis and the a posteriori error estimation for eigenvalue 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. 510 Eigenwertproblem Fehlerabschätzung Interpolation Interpolationsoperator Singularität <Mathematik> Clement-type interpolation a posteriori error estimation corner singularities non-linear eigenvalue problems spectral theory two-dimensional manifolds unit sphere urn:nbn:de:swb:ch1-200600805 3-8325-1249-7 Technische Universität Chemnitz dgg Technische Universität Chemnitz, Chemnitz Logos Verlag Berlin pbl Logos Verlag Berlin, Chemnitz Cornelia Pester Dipl.-Math. 2006-07-08 aut Thomas Apel Professor dgs rev Arnd Meyer Professor rev Serge Nicaise Professor rev eng 2005-11-25 2006-04-21 born digital doctoral_thesis