대한수학회지 (Journal of the Korean Mathematical Society)

  • 제34권3호
  • /
  • Pages.515-531
  • /
  • 1997
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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)
  • 발행 : 1997.08.01
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초록

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.

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참고문헌

  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
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  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