Mixed enrichment for the finite element method in heterogeneous media

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

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.
• Public URL: https://durham-repository.worktribe.com/output/1444691