Error estimates for a single-phase nonlinear Stefan problem in one space dimension

H. Y. Lee; M. R. Ohm; J. Y. Shin

Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1997; 34(3): 661-672

Printed September 1, 1997

Error estimates for a single-phase nonlinear Stefan problem in one space dimension

H. Y. Lee, M. R. Ohm, and J. Y. Shin

Kyungsung University, Dongseo University and Pukyong National University

Abstract

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Abstract

In this paper we introduce the semidiscrete solution of a single-phase nonlinear Stefan problem. We analyze the optimal convergence of the semidiscrete solution in $ H^1 $ and $ H^2 $ normed spaces and also we derive the error estimates in $ L^2 $ normed space.

Keywords: error analysis, semidiscrete approximation

MSC numbers: 65M15, 65N30