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Directional enrichment functions for finite element solutions of transient anisotropic diffusion

Bahssini, Abderrahim; Izem, Nouh; Mohamed, M. Shadi; Seaid, Mohammed

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Authors

Abderrahim Bahssini

Nouh Izem

M. Shadi Mohamed



Abstract


The present study proposes a novel approach for efficiently solving an anisotropic transient diffusion problem using an enriched finite element method. We develop directional enrichment for the finite elements in the spatial discretization and a fully implicit scheme for the temporal discretization of the governing equations. Within this comprehensive framework, the proposed class of exponential functions as enrichment enhance the approximation of the finite element method by capturing the directional based behaviour of the solution. The incorporation of these enrichment functions leverages a priori knowledge about the anisotropic problem using the partition of unity technique, resulting in significantly improved approximation efficiency while retaining all the advantages of the standard finite element method. Consequently, the proposed approach yields accurate numerical solutions even on coarse meshes and with significantly fewer degrees of freedom compared to the standard finite element methods. Moreover, the choice of mesh coarseness remains independent of the anisotropy in the problem, enabling the use of the same mesh regardless of changes in the anisotropy. Using extensive numerical experiments, we consistently demonstrate the efficiency of the proposed method in attaining the desired levels of accuracy. Our approach not only provides reliable and precise solutions but also extends the capabilities of the finite element method to effectively address aspects of the heterogeneous anisotropic transient diffusion problems that were previously considered ineffective when using this method.

Citation

Bahssini, A., Izem, N., Mohamed, M. S., & Seaid, M. (in press). Directional enrichment functions for finite element solutions of transient anisotropic diffusion. Computers and Mathematics with Applications, 163, 42-55. https://doi.org/10.1016/j.camwa.2024.03.016

Journal Article Type Article
Acceptance Date Mar 10, 2024
Online Publication Date Mar 26, 2024
Deposit Date Apr 16, 2024
Publicly Available Date Apr 16, 2024
Journal Computers & Mathematics with Applications
Print ISSN 0898-1221
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 163
Pages 42-55
DOI https://doi.org/10.1016/j.camwa.2024.03.016
Public URL https://durham-repository.worktribe.com/output/2378589

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