Workshop Numerical Analysis for Singularly Perturbed Problems
(dedicated to the 60th birthday of Martin Stynes)

Workshop Singularly Perturbed Problems

Talks & Slides

Grid method for solving a Stefan-type problem

Lidia Pavlovna Shishkina (Institute of Mathematics and Mechanics, Russian Academy of Sciences)

A research result is considered that is fulfilled joint with G.I. Shishkin, M. Stynes, K. Cronin, M. Viscor (see [1]). A grid method is has been developed to solve a Stefan-type problem (for its description see [2]) that describes the advanced stage of the high intensity drying process of wet granular materials in the hot air flow (a mathematical model of such a process is written in [3]). The Stefan-type problem under consideration is an initial-boundary value problem for a parabolic reaction-diffusion equation on a composite domain with a moving interface boundary. At the moving boundary between the two subdomains, an interface condition is prescribed for the solution of the problem and its derivatives. A nonlinear finite difference scheme is constructed that approximates the initial-boundary value problem. An iterative Newton-type method for the solution of the nonlinear difference scheme and a numerical method for the convergence analysis of the computed discrete solutions are both developed. Numerical experiments have been showed that the constructed scheme converges with the convergence order close to one.

[1] G. Shishkin, L. Shishkina, K. Cronin, M. Stynes and M. Viscor. A Numerical Method for a Stefan-Type Problem. Mathematical Modelling and Analysis. 2011. V. 16, No 1, pp. 119--142.
[2] G.I. Shishkin. On a problem of Stefan type with discontinuous moving boundary. Soviet Math. Dokl.. 1975. V. 16, No 5, pp. 1409--1412.
[3] G.I. Shishkin, L.P Shishkina, K. Cronin, M. Stynes and M. Viscor. Heat-mass-transfer for granular drying mathematical modelling. In Mathematical and Informational Technologies in Management, Engineering and Education, Proceedings of the 3-d International Scientific Conference, pp. 16--23. Ekaterinburg: UGTU/UPI, 2009. (in Russian).

Last change: 21 November 2011