Multi-level methods for degenerated problems with applications to p-versions of the fem [Elektronische Ressource] / vorgelegt von Sven Beuchler

Multi level methods for degenerated problems withapplications top versions of the femVon der Fakultat¨ fur¨ Mathematik der Technischen Universitat¨ ChemnitzgenehmigteD i s s e r t a t i o nzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegtvon Dipl. Math. Sven Beuchlergeboren am 24. Juli 1975 in Karl Marx Stadteingereicht am 5. 2. 2003Gutachter: Prof. Dr. Arnd MeyerProf. Dr. Arnold ReuskenPD Dr. Markus MelenkTag der Verteidigung: 11. 7. 2003PrefaceMany physical problems lead to boundary value problems for partial differential equations whichcan be solved with theh−,hp−, andp−version of the finite element method. Such a discretiza tion leads to a system of linear algebraic equations. One of the most efficient methods in order tosolve systems of linear algebraic equations resulting fromp version finite element discretizationsof elliptic boundary value problems is the conjugate gradient method with domain decomposi tion preconditioners. The ingredients of such a preconditioner are a preconditioner for the Schurcomplement, a preconditioner related to the Dirichlet problems in the sub domains, and an ex tension operator from the boundaries of the sub domains into their interior.The aim of this monograph is to develop a preconditioner for the problems in the sub domains.