The partition of unity finite element method: Basic theory and applications

doi:10.1016/S0045-7825(96)01087-0

Computer Methods in Applied Mechanics and Engineering

Volume 139, Issues 1–4, 15 December 1996, Pages 289-314

https://doi.org/10.1016/S0045-7825(96)01087-0 Get rights and content

Abstract

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 equation under consideration to construct effective and robust methods. Although the method and its theory are valid in n 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 PUFEM and conclude this paper with some open questions concerning implementational aspects of the PUFEM.

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¹: Partially supported by the US Office of Naval Research under grant N00014-90-J1030 and by the National Science Foundation under grant DMS-91-20877.

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The partition of unity finite element method: Basic theory and applications

Abstract

Comput. Methods Appl. Mech. Engrg.

J. Comput. Phys.

Integral Operators in the Theory of Linear Partial Differential Equations

A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems

SIAM J. Sci. Comput.

Table of Integrals, Series and Products

Boundary Methods: An Algebraic Theory

Linear Integral Equations

On generalized finite element methods