• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.357-364
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• 2003

A fully discrete $H^1-mixed$ finite element approximation for the single-phase Stefan problem is introduced and the unique existence of the approximation is established. And some numerical experiments are given.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.55-69
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• 1999

In this paper we analyze the error estimates for a single-phase nonlinear Stefan problem with Neumann boundary conditions. We apply the modified Crank-Nicolson method to get the optimal order of error estimates in the temporal direction.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.251-264
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• 2004

We introduce a semidiscrete mixed finite element approximation for the single-phase linear Stefan problem and show the unique existence of the approximation. And the optimal rate of convergence in $L^2$ and $H^1$ norms are derived.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.795-809
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• 2001

In this paper, we apply finite element Galerkin method to a single-ohase linear Stefan problem with a forcing term. We apply the extrapolated Crank-Nicolson method to construct the fully discrete approximation and we derive optimal error estimates in the temporal direction in $L^2$, $H^1$ spaces.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.191-207
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• 2007

Based on a mixed Galerkin approximation, we construct the fully discrete approximations of $U_y$ as well as U to a single-phase quasilinear Stefan problem with a forcing term in non-divergence form. We prove the optimal convergence of approximation to the solution {U, S} and the superconvergence of approximation to $U_y$.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.185-199
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• 2003

In this paper, we apply finite element Galerkin method to a single-phase quasi-linear Stefan problem with a forcing term. We consider the existence and uniqueness of a semidiscrete approximation and optimal error estimates in $L_2$, $L_{\infty}$, $H_1$ and $H_2$ norms for semidiscrete Galerkin approximations we derived.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.348-355
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• 1992

Casting structures and properties are determined by the solidification speed in the metal mold. The heat transfer characteristics of the interface between the mold and the casting is one of the major factors that control the solidification speed. According to Sully's research, the thermal resistance exists due to the air-gap formation at the mold-casting interface during the freezing process and the interface heat transfer coefficient is used to describe the degree of it. In this study, one-dimensional Stefan problem with air-gap resistance in the cylindrical geometry is considered and heat transfer characteristics is numerically examined. The temperature distribution and solidification speed are obtained by using the modified variable time step method. And the effects of the major parameters such as mold geometry, thermal conductivity, heat transfer coefficient and initial temperature of casting on the thermal characteristics are investigated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.6
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• pp.891-897
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• 1999

The heat transfer characteristics at the interface between the mold and the casting is one of the major factors for the solidification speed which determines the casting structures. The thermal resistance exists due to air gap formation at the mold/casting interface during the freezing process. In this study one dimensional Stefan problem with the air-gap resistance in the cylindrical mold is considered and the heat transfer characteristics is numerically examined by using the enthalpy method which is convenient in solving the Stefan problem with mushy zone. The present results agreed very well with those of previous papers. The effects of major parameters such as thermal conductivity, heat transfer coefficient of mold, on the thermal characteristics are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.39-48
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• 2013

This paper develops a 2-D moving least squares(MLS) difference method for Stefan problem by extending the 1-D version of the conventional method. Unlike to 1-D interfacial modeling, the complex topology change in 2-D domain due to arbitrarily moving boundary is successfully modelled. The MLS derivative approximation that drives the kinetics of moving boundary is derived while the strong merit of MLS Difference Method that utilizes only nodal computation is effectively conserved. The governing equations are differentiated by an implicit scheme for achieving numerical stability and the moving boundary is updated by an explicit scheme for maximizing numerical efficiency. Numerical experiments prove that the MLS Difference Method shows very good accuracy and efficiency in solving complex 2-D Stefan problems.