Die p- und hp-Version der Finite-Elemente-Methode oder. Lohnen sich hoeherwertige Elemente

Attractive new possibilities of quality control and improvement of the results can be achieved by using higher order shape functions in finite element computations. During the last few years a systematic approach to a new generation of finite element software has been developed allowing the polynomial degree of the shape functions to be varied freely over the mesh. After a discussion of the basic ideas it is shown in numerical examples how a balanced mesh construction and distribution of the polynomial degree yield robustness and superior accuracy of the new method.