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 - <p style="text-align: justify;">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.</p>