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The Partition of Unity Finite Element Method: Basic Theory and Applications

by J. M. Melenk and I. Babuska

(Report number 1996-01)

Abstract
The paper presents the basic ideas and the mathematical foundation of the partition of unity finite element method (\PU). We will show how the \PU can be used to employ the structure of the differential equation under consideration to construct effective and robust methods. Although the method and its theory are valid in emn/em dimensions, a detailed and illustrative analysis will be given for a one dimensional model problem. We identify some classes of non-standard problems which can profit highly from the advantages of the \PU and conclude this paper with some open questions concerning implementational aspects of the \PU.

Keywords: Finite element method, meshless finite element method, robust finite element methods, finite element methods for highly oscillatory solutions

@Techreport{MB96_184,
  author = {J. M. Melenk and I. Babuska},
  title = {The Partition of Unity Finite Element Method: Basic Theory and Applications},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-01.pdf },
  year = {1996}
}

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