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ON SUPERCONVERGENCE RESULTS AND NEGATIVE NORM ESTIMATES FOR A UNIDIMENSIONAL SINGLE-PHASE STEFAN PROBLEM

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Title ON SUPERCONVERGENCE RESULTS AND NEGATIVE NORM ESTIMATES FOR A UNIDIMENSIONAL SINGLE-PHASE STEFAN PROBLEM
 
Creator JONES, L
PANI, AK
 
Subject galerkin methods
 
Description 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 H-1-Galerkin method is then applied to estimate the quadratic nonlinear term effectively and optimal estimates in L(infinity), L(2), H-1 and H-2- 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 H-1- Galerkin approximations to nonlinear parabolic equations are not available in the literature, the present study has an added significance.
 
Publisher MARCEL DEKKER INC
 
Date 2011-08-18T11:18:56Z
2011-12-26T12:55:43Z
2011-12-27T05:42:10Z
2011-08-18T11:18:56Z
2011-12-26T12:55:43Z
2011-12-27T05:42:10Z
1995
 
Type Article
 
Identifier NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 16(1-2), 153-175
0163-0563
http://dx.doi.org/10.1080/01630569508816611
http://dspace.library.iitb.ac.in/xmlui/handle/10054/9995
http://hdl.handle.net/10054/9995
 
Language en