Convergence of the Crank-Nicolson-Galerkin finite element method for a   class of nonlocal parabolic systems with moving boundaries
  The aim of this paper is to establish the convergence and error bounds to the fully discrete solution for a class of nonlinear systems 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 elements methods are investigated. 
Rui M.P. Almeida and Jos\'e C.M. Duque and Jorge Ferreira and Rui J.   Robalo
math.NA