Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

ERROR ESTIMATES FOR MIXED FINITE ELEMENT APPROXIMATIONS TO A LINEAR STEFAN PROBLEM

  • Ann, M.H. (received her BS degree from Pusan National University and her degree of Master of Education from Pukyong National University) ;
  • Shin, J.Y. (Division of Mathematical Sciences, Pukyong National University)
  • Published : 2004.05.01

⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. IMA J. Numer. Anal. v.9 A priori error estimates in $H^1$ and $H^2$ norms for Galerkin approa~imations to a single phase nonlinear Stefan problem in one space dimension P. C. Das;A. K. Pani
  2. J. Math. Anal. Appl. v.72 Free boundary problems for nonlinear parabolic equations with nonlinear free boundary conditions A. Fasano;M. Primicerlo
  3. Numer. Methods Partial Differential Equations v.13 Galerkin method for a Stefan-type problem in one space dimension L. Jones;T. Doss, A. K. Pani;S. Padhy
  4. Appl. Numer. Math. v.26 Error estimates for a single-phase quasilinear Stefan problem in one space dimension H. Y. Lee;J. R. Lee
  5. J. Korean Math. Soc. v.34 Error estimates for a single-phase nonlinear Stefan problem in one space dimension H. Y. Lee;M. R. Ohm;J. Y. Shin
  6. Proc. Recent Adv. Numer. Anal. Finite element approximations to the one-dimensional Stefan problem J. A. Nitsche;C. de Boor(ed.);G. Golub(ed.)
  7. Free boundary problems v.1 A finite element method for parabolic free boundary problems J. A. Nitsche;E. Magenes(ed.)
  8. J. Math. Anal. and Appl. v.199 $H^1$ estimates of optimal orders for Galerkin methods to one dimensional Stefan problems M. R. Ohm
  9. Appl. Math. Comp. v.143 Error analysis of a mixed finite element approximation of a linear Stefan problem H. Y. Lee;M. R. Ohm;J. Y. Shin
  10. A mixed finite element method for a single phase Stefan problem A. K. Pani
  11. IMA J. Numer. Anal. v.11 A finite element Galerkin method for a unidimensional single-phase nonlinear Stefan problem with Dirichlet boundary conditions A. K. Pani;P. C. Das
  12. IMA. J.Numer. Anal. v.11 A priori error estimates for a single-phase quasilinear Stefan problem in one dimension A. K. Pani;P. C. Das
  13. Numer. Funct. Anal. Optim. v.12 no.1;2 A finite element method for a single phase semilinear Stefan problem in one space dimension A. K. Pani;P. C. Das