Mixed enrichment for the finite element method in heterogeneous media

Diwan, G.C.; Mohamed, M.S.; Seaid, M.; Trevelyan, J.; Laghrouche, O.

doi:10.1002/nme.4795

Mixed enrichment for the finite element method in heterogeneous media

Diwan, G.C.; Mohamed, M.S.; Seaid, M.; Trevelyan, J.; Laghrouche, O.

Authors

G.C. Diwan

M.S. Mohamed

Dr Mohammed Seaid m.seaid@durham.ac.uk
Associate Professor

Professor Jon Trevelyan jon.trevelyan@durham.ac.uk
Emeritus Professor

O. Laghrouche

Abstract

Problems of multiple scales of interest or of locally nonsmooth solutions may often involve heterogeneous media. These problems are usually very demanding in terms of computations with the conventional finite element method. On the other hand, different enriched finite element methods such as the partition of unity, which proved to be very successful in treating similar problems, are developed and studied for homogeneous media. In this work, we present a new idea to extend the partition of unity finite element method to treat heterogeneous materials. The idea is studied in applications to wave scattering and heat transfer problems where significant advantages are noted over the standard finite element method. Although presented within the partition of unity context, the same enrichment idea can also be extended to other enriched methods to deal with heterogeneous materials.

Citation

Diwan, G., Mohamed, M., Seaid, M., Trevelyan, J., & Laghrouche, O. (2015). Mixed enrichment for the finite element method in heterogeneous media. International Journal for Numerical Methods in Engineering, 101(1), 54-78. https://doi.org/10.1002/nme.4795

Journal Article Type	Article
Acceptance Date	Aug 23, 2014
Online Publication Date	Oct 1, 2014
Publication Date	Jan 6, 2015
Deposit Date	Oct 3, 2014
Publicly Available Date	Oct 28, 2014
Journal	International Journal for Numerical Methods in Engineering
Print ISSN	0029-5981
Electronic ISSN	1097-0207
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	101
Issue	1
Pages	54-78
DOI	https://doi.org/10.1002/nme.4795
Keywords	Finite element method, Partition of unity method, Acoustic wave scattering, Transient heat transfer, Composite materials, Heterogeneous media, Multiscale.

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Copyright Statement
This is the accepted version of the following article: Diwan G. C., Mohamed M. S., Seaid M., Trevelyan J., and Laghrouche O. (2014), Mixed enrichment for the finite element method in heterogeneous media, International Journal for Numerical Methods in Engineering, 101 (1): 54-78, which has been published in final form at http://dx.doi.org/10.1002/nme.4795. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.