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The partition‐of‐unity method for linear diffusion and convection problems: accuracy, stabilization and multiscale interpretation
Author(s) -
Munts E. A.,
Hulshoff S. J.,
des Borst R.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.608
Subject(s) - partition of unity , exponential function , convection–diffusion equation , partition (number theory) , mathematics , diffusion , function (biology) , polynomial , convection , finite element method , mathematical analysis , thermodynamics , physics , combinatorics , evolutionary biology , biology
We investigate the effectiveness of the partition‐of‐unity method (PUM) for convection–diffusion problems. We show that for the linear diffusion equation, an exponential enrichment function based on an approximation of the analytic solution leads to improved accuracy compared to the standard finite‐element method. It is illustrated that this approach can be more efficient than using polynomial enrichment to increase the order of the scheme. We argue that the PUM enrichment, can be interpreted as a subgrid‐scale model in a multiscale framework, and that the choice of enrichment function has consequences for the stabilization properties of the method. The exponential enrichment is shown to function as a near optimal subgrid‐scale model for linear convection. Copyright © 2003 John Wiley & Sons, Ltd.