• Title, Summary, Keyword: Steklov mollifier

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

  • Chung, S.K.;Pani, A.K.;Park, M.G.
    • Journal of the Korean Mathematical Society
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    • v.34 no.3
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    • pp.515-531
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    • 1997
  • 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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