East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON THE FINITE DIFFERENCE OPERATOR $l_{N^2}$(u, v)

  • Woo, Gyung-Soo (Department of Applied Mathematics Changwon National University) ;
  • Lee, Mi-Na (Department of Applied Mathematics Changwon National University) ;
  • Seo, Tae-Young (Department of Mathematics Pusan National University)
  • Published : 2000.06.25
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Abstract

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.

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