Volume 6, Issue 4
Numerical Analysis for a Nonlocal Parabolic Problem

M. Mbehou, R. Maritz & P.M.D. Tchepmo

East Asian J. Appl. Math., 6 (2016), pp. 434-447.

Published online: 2018-02

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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.

  • Keywords

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

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-434, author = {}, title = {Numerical Analysis for a Nonlocal Parabolic Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.260516.150816a}, url = {http://global-sci.org/intro/article_detail/eajam/10811.html} }
TY - JOUR T1 - Numerical Analysis for a Nonlocal Parabolic Problem JO - East Asian Journal on Applied Mathematics VL - 4 SP - 434 EP - 447 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.260516.150816a UR - https://global-sci.org/intro/article_detail/eajam/10811.html KW - Convergence, numerical simulation, Crank-Nicolson schemes, Galerkin finite element method, nonlinear parabolic equation, nonlocal diffusion term. AB -

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.

M. Mbehou, R. Maritz & P.M.D. Tchepmo. (2020). Numerical Analysis for a Nonlocal Parabolic Problem. East Asian Journal on Applied Mathematics. 6 (4). 434-447. doi:10.4208/eajam.260516.150816a
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