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

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

http://hdl.handle.net/10400.6/9665

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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.