The Crank–Nicolson–Galerkin Finite Element Method for a Nonlocal Parabolic Equation with Moving Boundaries

The aim of this article is to establish the convergence and error bounds for the fully discrete solutions of a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries, using a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of a...

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Bibliographic Details
Main Author: Almeida, Rui M.P. (author)
Other Authors: Duque, José C. M. (author), Ferreira, Jorge (author), Robalo, Rui J. (author)
Format: article
Language:eng
Published: 2020
Subjects:
Nonlinear parabolic system
Nonlocal diffusion term
Reaction–diffusion
Convergence
Numerical simulation
Crank–Nicolson
Finite element method
Online Access:http://hdl.handle.net/10400.6/9665
Country:Portugal
Oai:oai:ubibliorum.ubi.pt:10400.6/9665
Description
Summary:The aim of this article is to establish the convergence and error bounds for the fully discrete solutions of a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries, using a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite element methods are investigated.

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