Reliable numerical schemes for a linear diffusion equation on a nonsmooth domain - (:unkn) unknown (My University, 2010)
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.
Keywords: African Research