Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

CONVERGENCE OF FINITE DIFFERENCE METHOD FOR THE GENERALIZED SOLUTIONS OF SOBOLEV EQUATIONS

  • Chung, S.K. (Department of Mathematics Education Seoul National University) ;
  • Pani, A.K. (Department of Mathematics Indian Institute of Technology) ;
  • Park, M.G. (Department of Mathematics Education Seoul National University)
  • Published : 1997.08.01
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Abstract

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.

Keywords

References

  1. Math. Comp. v.36 Superconvergence of a finite element approxiamtion to the solution of a Sobolev equation in a single space variable D. N. Arnold;J. Douglas, Jr.;V. Thomee
  2. Numer. Math. v.16 Bounds for a class of linear functionals with applications to Hermite interpolation J. H. Bramble;S. R. Hilbert
  3. The finite element method for elliptic problems P. G. Ciarlet
  4. SIAM J. Numer. Anal. v.12 Numerical solution of Sobolev partial differential equations R. E. Ewing
  5. SIAM J. Numer. Anal. v.15 Time-stepping Galerkin methods for nonlinear Sobolev partial differential equations R. E. Ewing
  6. Aequationes Math. v.14 Galerkin approximations to non-linear pseudo-parabolic partial differential equations W. H. Ford
  7. Math. Comp. v.27 Stability and converegence of difference approximations to pseudo-parabolic partial differential equations W. H. Ford;T. W. Ting
  8. SIAM J.Numer. Anal. v.11 Uniform error estimates for difference approximations to nonlinear pseudo-parabolic partial differential equations W. H. Ford;T. W. Ting
  9. IMA J. Numer. Anal. v.7 Convergence of a finitedifference scheme for secondorder hyperbolic equations with variable coefficients, B. S. Jovanovic;L. D. Ivanovic;E. E. Suli
  10. J. Math. Anal. Appl. v.165 Finite element methods for nonlinear Sobolev equations with nonlinear boundary conditions Y. Lin;T. Zhang
  11. Numer. Math. v.47 Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension M. T. Nakao
  12. CMAMR191 On convergence of finite difference schemes for generalized solutions of parabolic and hyperbolic partialdifferential equations A. K. Pani;S. K. Chung;R. S. Anderssen
  13. CMAMR391 On convergence of finite difference schemes for generalized solutions of parabolic and hyperbolic integrodifferential equations A. K. Pani;S. K. Chung;R. S. Anderssen