On superconvergence results and negative norm estimates for a unidimensional single phase Stefan problem

Jones, L. ; Pani, A. K. (1995) On superconvergence results and negative norm estimates for a unidimensional single phase Stefan problem Numerical Functional Analysis and Optimization, 16 (1-2). pp. 153-175. ISSN 0163-0563

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Official URL: http://www.tandfonline.com/doi/abs/10.1080/0163056...

Related URL: http://dx.doi.org/10.1080/01630569508816611

Abstract

Based on Landau-type transformation, a unidimensional single phase Stefan problem is transformed into a system consisting of parabolic equation with a quadratic nonlinear term and two ordinary differential equations. An Hl-Galerkin method is then applied to estimate the quadratic nonlinear term effectively and optimal estimates in L, L2, H1 and H2 norms are obtained without quasiuniformity condition on the finite element mesh. Further using quasiprojection technique, negative norm estimates and superconvergence results are derived. As a result, Galerkin approximation for the free boundary exhibits a superconvergence phenomenon. Since the superconvergence results for the Hl-Galerkin approximations to nonlinear parabolic equations are not available in the literature, the present study has an added significance.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Group.
ID Code:81981
Deposited On:09 Feb 2012 04:33
Last Modified:09 Feb 2012 04:33

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