Expert-System-Like Feedback Approach in the hp-Version of the Finite Element Method

摘要

It has been theoretically shown that exponential rate of convergence in the energy norm can be obtained by a proper combination of the h- and p- extension of the finite element method for essentially all engineering problems in plane elasticity, including those with singularities in the exact solution. In this paper we present an expert system frame, which guides the user to an optimal selection of the mesh and degree distribution. After a crude preliminary computation the expert system predicts the performance of various mesh and degree combinations and provides the analyst with rational support for his decisions about the mesh design. Numerical examples show that the suggested approach gives superior results with the minimum effort in human data preparation and computer time. Keywords: Adaptive methods; and Error estimations.