Numerical Analysis for a Nonlocal Parabolic Problem

Numerical Analysis for a Nonlocal Parabolic Problem

Year:    2016

East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 4 : pp. 434–447

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.260516.150816a

East Asian Journal on Applied Mathematics, Vol. 6 (2016), Iss. 4 : pp. 434–447

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Convergence numerical simulation Crank-Nicolson schemes Galerkin finite element method nonlinear parabolic equation nonlocal diffusion term.

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