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Reliable numerical schemes for a linear diffusion equation on a nonsmooth domain

✍ Scribed by Pius W.M. Chin; Jules K. Djoko; Jean M.-S. Lubuma

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 475 KB
Volume: 23
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2010.01.008

No coin nor oath required. For personal study only.

✦ Synopsis

The solution of a linear reaction-diffusion equation on a non-convex polygon is proved to be globally regular in a suitable weighted Sobolev space. This result is used to design an optimally convergent Fourier-Finite Element Method (FEM) where the mesh size is suitably refined. Furthermore, the coupled Non-Standard Finite Difference Method (NSFDM)-FEM is presented as a reliable scheme that replicates the essential properties of the exact solution.

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