• 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.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.815-834
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• 1995

Let $\Omega$ be a rectangular domain in $R^2$ with boundary $\partial\Omega$, and T be a positive real number such that $0 < T < \infty$.