Geodesic
On the inevitable error of the method of nets
Matematičeskie zametki, Tome 4 (1968) no. 6, pp. 621-627.

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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). 
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     author = {E. A. Volkov},
     title = {On the inevitable error of the method of nets},
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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/