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Numerical Analysis for a Nonlocal Parabolic Problem

Published online by Cambridge University Press:  19 October 2016

M. Mbehou*
Affiliation:
Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South Africa Department of Mathematics, University of Yaounde I, Cameroon
R. Maritz
Affiliation:
Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South Africa
P.M.D. Tchepmo
Affiliation:
Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South Africa
*
*Corresponding author. Email address:[email protected] (M. Mbehou)
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Abstract

This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in finite time are presented. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

Type
Research Article
Copyright
Copyright © Global-Science Press 2016 

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