Geodesic
On the inevitable error of the method of nets
Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 621-627 
E. A. Volkov. On the inevitable error of the method of nets. Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 621-627. http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a0/
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     author = {E. A. Volkov},
     title = {On the inevitable error of the method of nets},
     journal = {Matemati\v{c}eskie zametki},
     pages = {621--627},
     year = {1968},
     volume = {4},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_6_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that no matter what the solution of an arbitrary boundary-value problem for the two-dimensional Laplace equation, unless it is a special fourth-degree harmonic polynomial, the rate of convergence of the method of square nets using the operator for computation of the four-point arithmetic mean can never be better than $h^2$ (where $h$ is the spacing of the net).