Yahia S. Halabi, "Simulation of continuously deforming parabolic problems by Galerkin finite-elements method", International Journal of Mathematics and Mathematical Sciences, vol. 9, Article ID 974769, 6 pages, 1986. https://doi.org/10.1155/S0161171286000728
Simulation of continuously deforming parabolic problems by Galerkin finite-elements method
A general numerical finite element scheme is described for parabolic problems with phase change wherein the elements of the domain are allowed to deform continuously. The scheme is based on the Galerkin approximation in space, and finite difference approximation for the time derivatives. The numerical scheme is applied to the two-phase Stefan problems associated with the melting and solidification of a substance. Basic functions based on Hermite polynomials are used to allow exact specification of flux-latent heat balance conditions at the phase boundary. Numerical results obtained by this scheme indicates that the method is stable and produces an accurate solutions for the heat conduction problems with phase change; even when large time steps used. The method is quite general and applicable for a variety of problems involving transition zones and deforming regions, and can be applied for one multidimensional problems.
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