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Numerical Analysis for a Nonlocal Parabolic Problem

Part of:Partial differential equations, boundary value problems

Published online by Cambridge University Press:  19 October 2016

M. Mbehou,
R. Maritz and
P.M.D. Tchepmo
M. Mbehou*
Affiliation:
Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South AfricaDepartment 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:mohamm@unisa.ac.za (M. Mbehou)

Abstract

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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.

Keywords

Convergencenumerical simulationCrank-Nicolson schemesGalerkin finite element methodnonlinear parabolic equationnonlocal diffusion term

MSC classification

Secondary:65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 4 , November 2016, pp. 434 - 447
Copyright
Copyright © Global-Science Press 2016 

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