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

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

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