TY  - THES
T1  - Finite element methods with local Trefftz trial functions
A1  - Weißer,Steffen
Y1  - 2012/10/23
N2  - In the development of numerical methods for boundary value problems, the requirement of flexible mesh handling gains more and more importance. The available work deals with a new kind of conforming finite element methods on polygonal/polyhedral meshes. The idea is to use basis functions which are defined implicitly as local solutions of the underlying homogeneous problem with constant coefficients. They are referred to local Trefftz functions. These local problems are treated by means of boundary integral equations and are approximated by the use of the boundary element method in the numerics. The method is applied to the stationary diffusion equation, where lower as well as higher order basis functions are introduced in two space dimensions. The convergence is analysed with respect to the H^1- as well as the L_2-norm and rates of convergence are proven. In case of non-constant diffusion coefficients, a special approximation is proposed. Beside the uniform refinement, an adaptive strategy is given which makes use of the residual error estimator and an introduced refinement procedure. The reliability of the residual error estimate is proven on polygonal meshes. Finally, the generalization to arbitrary polyhedral meshes with polygonal faces is discussed. All theoretical results and considerations are confirmed by numerical experiments.
KW  - Finite-Elemente-Methode
KW  - Randelemente-Methode
KW  - Adaptives Verfahren
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2012/4968
ER  -