scholarly journals Fully Discrete Error Estimation by the Method of Lines for a Nonlinear Parabolic Problem

2003 ◽  
Vol 48 (2) ◽  
pp. 129-151 ◽  
Author(s):  
Tomáš Vejchodský
Keyword(s):  
Error Estimation ◽  
Parabolic Problem ◽  
Method Of Lines ◽  
Fully Discrete ◽  
Nonlinear Parabolic Problem ◽  
Nonlinear Parabolic ◽  
The Method Of Lines

Numerical Analysis for a Nonlocal Parabolic Problem

2016 ◽  
Vol 6 (4) ◽  
pp. 434-447 ◽  
Author(s):  
M. Mbehou ◽  
R. Maritz ◽  
P.M.D. Tchepmo
Keyword(s):  
Finite Element ◽  
Parabolic Problem ◽  
Reaction Diffusion ◽  
Finite Element Approximation ◽  
Reaction Diffusion Equation ◽  
Element Approximation ◽  
Galerkin Finite Element ◽  
Fully Discrete ◽  
Nonlinear Reaction Diffusion Equation ◽  
Nonlinear Parabolic

AbstractThis 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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