The Crank–Nicolson–Galerkin finite element method for a nonlocal parabolic equation with moving boundaries | Zendy

Almeida Rui M. P. | Zendy; Duque José C. M. | Zendy; Ferreira Jorge | Zendy; Robalo Rui J. | Zendy

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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

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