1549301742-The_Theory_of_Difference_Schemes__Samarskii

Some properties of difference elliptic operators 277

(12)

and

(13)

with

(14) [y, v] = (y, v) + hi h2 [

4

y(O, 0) v(O, 0) + y(O, 12 ) v(O, 12 )

+ y(l 1 , 0) v(l 1 , 0) + y(l 1 , 12 ) v(l 1 , 12 )]

N2-I

+ ';^1 L [y(O, i 2 h 2 ) v(O, i 2 h 2 )

i2=2

N 1 -J

+~^2 2= [y(ilhl,o)v(ilhl,o)

'1 =2

the inner product (y, v) being understood in the sense of (7).

0

2. Properties of difference operators. Introduce the space rlh of all grid
   functions defined on the grid wh = wh + ih and vanishing on the boundary
   ih and the space s:th comprising all the functions defined on w h. The inner
   product in the space s:th is defined to be

(15) (y,v)= L y(x)v(x)h 1 h 2 •
xEwh