Error estimates for the multidimensional two-phase Stefan problem

Authors:
Joseph W. Jerome and Michael E. Rose

Journal:
Math. Comp. **39** (1982), 377-414

MSC:
Primary 65M60; Secondary 65M05, 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1982-0669635-2

MathSciNet review:
669635

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Abstract: In this paper we derive rates of convergence for regularizations of the multidimensional two-phase Stefan problem and use the regularized problems to define backward-difference in time and piecewise-linear in space Galerkin approximations. We find an rate of convergence of order in the -regularization and an rate of convergence of order in the Galerkin estimates which leads to the natural choices , , and a resulting rate of convergence of the numerical scheme to the solution of the differential equation. An essentially rate is demonstrated when and in our Galerkin scheme under a boundedness hypothesis on the Galerkin approximations. The latter result is consistent with computational experience.

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0669635-2

Article copyright:
© Copyright 1982
American Mathematical Society