SIAM Journal on Scientific and Statistical Computing
A note on the use of the isotherm migration method
Journal of Computational and Applied Mathematics
The phase-field method in the sharp-interface limit: a comparison between model potentials
Journal of Computational Physics
A variable time step Galerkin method for a one-dimensional Stefan problem
Applied Mathematics and Computation
The numerical solution of one-phase classical Stefan problem
Journal of Computational and Applied Mathematics
A moving mesh finite element method for the two-dimensional Stefan problems
Journal of Computational Physics
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The enthalpy method is exploited in tackling a heat transfer problem involving a change of state. The resulting governing equation is then solved with a hybrid finite element - boundary element technique known as the Green element method (GEM). Two methods of approximation are employed to handle the time derivative contained in the discrete element equation. The first involves a finite difference method, while the second utilizes a Galerkin finite element approach. The performance of both methods are assessed with a known closed form solution. The finite element based time discretization, despite its greater challenge, yields less reliable numerical results. In addition a numerical stability test of both methods based on a Fourier series analysis explain the dispersive characters of both techniques, and confirms that replication of correct results is largely attributed to their ability to handle the harmonics of small wavelengths which are usually dominant in the vicinity of a front.