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p ‐version of the generalized FEM using mesh‐based handbooks with applications to multiscale problems
Author(s) -
Strouboulis Theofanis,
Zhang Lin,
Babuška Ivo
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1017
Subject(s) - finite element method , robustness (evolution) , partition of unity , laplace operator , polygon mesh , mathematics , vertex (graph theory) , boundary value problem , computer science , mathematical optimization , algorithm , mathematical analysis , structural engineering , geometry , discrete mathematics , graph , engineering , biochemistry , chemistry , gene
In this paper, we analyse the p ‐convergence of a new version of the generalized finite element method (generalized FEM or GFEM) which employs mesh‐based handbook functions which are solutions of boundary value problems in domains extracted from vertex patches of the employed mesh and are pasted into the global approximation by the partition of unity method (PUM). We show that the p ‐version of our GFEM is capable of achieving very high accuracy for multiscale problems which may be impossible to solve using the standard FEM. We analyse the effect of the main factors affecting the accuracy of the method namely: (a) The data and the buffer included in the handbook domains, and (b) The accuracy of the numerical construction of the handbook functions. We illustrate the robustness of the method by employing as model problem the Laplacian in a domain with a large number of closely spaced voids. Similar robustness can be expected for problems of heat‐conduction and elasticity set in domains with a large number of closely spaced voids, cracks, inclusions, etc. Copyright © 2004 John Wiley & Sons, Ltd.