### 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 language | English (US) |
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Pages (from-to) | 377-414 |

Number of pages | 38 |

Journal | Mathematics of Computation |

Volume | 39 |

Issue number | 160 |

DOIs | |

Publication status | Published - Oct 1982 |

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### ASJC Scopus subject areas

- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics

### Cite this

*Mathematics of Computation*,

*39*(160), 377-414. https://doi.org/10.1090/S0025-5718-1982-0669635-2