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The Crank–Nicolson–Galerkin finite element method for a nonlocal parabolic equation with moving boundaries
Author(s) -
Almeida Rui M. P.,
Duque José C. M.,
Ferreira Jorge,
Robalo Rui J.
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21957
Subject(s) - mathematics , crank–nicolson method , finite element method , galerkin method , polynomial , partial differential equation , convergence (economics) , mathematical analysis , nonlinear system , transformation (genetics) , degree of a polynomial , numerical analysis , physics , thermodynamics , biochemistry , chemistry , quantum mechanics , gene , economics , economic growth
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. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1515–1533, 2015