Abstract
Based on Landau-type transformation, a Stefan problem with nonlinear free boundary condition is transformed into a system consisting of parabolic equation and the ordinary differential equations. Semidiscrete approximations are constructed. Optimal orders of convergence of semidiscrete approximation inL 2,H 1 andH 2 normed spaces are derived.
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References
M. J. Ahn and H. Y. Lee,Extrapolated Crank-Nicolson approximation for a linear Stefan problem with a forcing term, J. Appl. Math. and Computing(old:KJCAM) 8 (2001), 549–569.
P. C. Das and A. K. Pani,A priori error estimates in H 1 and H 2 norms for Galerkin approximations to a single-phase nonlinear Stefan problem in one dimensional space, IMA J. Numer. Anal. 9 (1989), 213–229.
A. Fasamo and M. Primicerio,Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions, J. Math. Anal. Appl. 72 (1979), 247–273.
H. Y. Lee, M. R. Ohm, and J. Y. Shin,Fully discrete approximation for a quasilinear Stefan problem with forcing term, Applied Mathematics and Computation 133 (2002), 461–478.
J. A. Nitsche,Finite element approximations to the one-dimensional Stefan problem. In: Jour. Proc. Recent Adv. Numer. Anal. (C. de Boor & G. Golub, eds.), New York, Academic Press 119–142, 1978.
J. A. Nitsche,A finite element method for parobolic free boundary problems, In: Free Boundary Problems I, (E. Magenes, Ed.) Rome: Institute Nationale di Alta Mathematica, 277–318, 1980.
M. R. Ohm, J. Y. Shin and H. Y. Lee,Error estimates for a single phase quasilinear Stefan problem with a forcing term, J. Applied Math. and Computing 11 (2003), 185–199
M. R. Ohm, J. Y. Shin, and H. Y. Lee,Error analysis of a mixed finite element approximation of a linear Stefan problem, Applied Mathematics and Computation 143 (2003), 485–500.
A. K. Pani and P. C. Das,A finite element Galerkin method for a unidimensional single phase nonlinear Stefan problem with Dirichlet boundary conditions, IMA J. Numer. Anal. 11 (1991), 99–113.
A. K. Pani and P. C. Das,A finite element method for a single phase semilinear Stefan problem in one space dimension, Numer. Funct. Anal. Optimiz. 12 (1991), 153–171.
A. K. Pani and P. C. Das,A priori error estimates for a single-phase quasilinear Stefan problem in one space dimension, IMA J. Numer. Anal. 11 (1991), 377–392.
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This research was supported by Kyungsung University Research Grants in 2002.
Hyun Yong Lee received her BS degree from Busan National University and Ph.D degree from University of Tennessee under the direction of Professor Ohannes Karakashian. She is a professor at Kyungsung University. Her research is focused on numerical analysis for partial differential equations.
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Lee, H.Y. A discrete finite element galerkin method for a unidimensional single-phase Stefan problem. JAMC 16, 165–181 (2004). https://doi.org/10.1007/BF02936159
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DOI: https://doi.org/10.1007/BF02936159