The Crank–Nicolson–Galerkin finite element method for a nonlocal parabolic equation with moving boundaries |
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| Authors: | Rui M P Almeida José C M Duque Jorge Ferreira Rui J Robalo |
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| Affiliation: | 1. Department of Mathematics, Faculty of Science, University of Beira Interior, Covilh?, Portugal;2. Department of Mathematical Sciences ‐ VCE, Center of Mathematics, FederalUniversity Fluminense ‐ UFF, Rio de Janeiro, Brazil |
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| Abstract: | 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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| Keywords: | nonlinear parabolic system nonlocal diffusion term reaction– diffusion convergence numerical simulation Crank– Nicolson finite element method |
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