FVM- and FEM-solution of elliptical boundary value problems in different coordinate systems

Abstract

In this paper several numerical concepts for the solution of elliptical boundary value problems will be compared with regard to their efficiency, computational load and accuracy. Especially regions which are images of rectangles and cuboids of coordinate transformations will be considered. I argue that it is thus possible to construct well structured discretisations which imply equation systems with very high solution properties. The approaches discussed will be tested with instructive examples in the light of their advantages and disadvantages. © Springer-Verlag Berlin Heidelberg 2007.