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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Error estimates for the multidimensional two-phase Stefan problem
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by Joseph W. Jerome and Michael E. Rose PDF
Math. Comp. 39 (1982), 377-414 Request permission


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 ${C^0}$ piecewise-linear in space Galerkin approximations. We find an ${L^2}$ rate of convergence of order $\sqrt \varepsilon$ in the $\varepsilon$-regularization and an ${L^2}$ rate of convergence of order $({h^2}/\varepsilon + \Delta t/\sqrt \varepsilon )$ in the Galerkin estimates which leads to the natural choices $\varepsilon \sim {h^{4/3}}$, $\Delta t \sim {h^{4/3}}$, and a resulting $O({h^{2/3}})\;{L^2}$ rate of convergence of the numerical scheme to the solution of the differential equation. An essentially $O(h)$ rate is demonstrated when $\varepsilon = 0$ and $\Delta t \sim {h^2}$ in our Galerkin scheme under a boundedness hypothesis on the Galerkin approximations. The latter result is consistent with computational experience.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 377-414
  • MSC: Primary 65M60; Secondary 65M05, 65M10
  • DOI:
  • MathSciNet review: 669635