THE PARTITION OF UNITY FINITE-ELEMENT METHOD - BASIC THEORY AND APPLICATIONS

The paper presents the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM). We will show how the PUFEM can be used to employ the structure of the differential equ ation under consideration to construct effective and robust methods. A lthough the method and its theory are valid in n dimensions, a detaile d and illustrative analysis win be given for a one-dimensional model p roblem. We identify some classes of non-standard problems which can pr ofit highly from the advantages of the PUFEM and conclude this paper w ith some open questions concerning implementational aspects of the PUF EM.