• East Asian mathematical journal
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• 제16권1호
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• pp.97-103
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• 2000

In this work, we consider a finite difference operator $L^2_N$ corresponding to $$Lu:=-(u_{xx}+u_{yy})\;in\;{\Omega},\;u=0\;on\;{\partial}{\Omega}$$, in $S_{h^2,1}$. We derive the relation between the absolute value of the bilinear form $l_{N^2}$(u, v) on $S_{h^2,1}{\times}S_{h^2,1}$ and Sobolev $H^1$ norms.

• 대한수학회지
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• 제34권3호
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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.