Error estimates for the multidimensional two-phase stefan problem

Joseph W. Jerome*, Michael E. Rose

*Corresponding author for this work

Research output: Contribution to journalArticle

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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 C° piecewise-linear in space Galerkin approximations. We find an L2 rate of convergence of order in the e-regularization and an L rate of convergence of order (h2/e + Δ t \6F) in the Galerkin estimates which leads to the natural choices £ ˜ Δ4t3, Δ; ˜ A4/3, and a resulting 0(ti2/3) L2 rate of convergence of the numerical scheme to the solution of the differential equation. An essentially 0(h) rate is demonstrated when e = 0 and Δ t ˜ h2 in our Galerkin scheme under a boundedness hypothesis on the Galerkin approximations. The latter result is consistent with computational experience.

Original languageEnglish (US)
Pages (from-to)377-414
Number of pages38
JournalMathematics of Computation
Volume39
Issue number160
DOIs
Publication statusPublished - Oct 1982

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ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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