Geodesic
The convergence in $W_2^2$ of a difference solution of the Dirichlet problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 470-474

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An estimate of the rate of convergence of the difference scheme considered in a net metric $W_2^2$, matched with the smoothness of the required solution, is established when the solution of the initial problem belongs to Sobolev spaces. 
@article{ZVMMF_1990_30_3_a12,
     author = {G. K. Berikelashvili},
     title = {The convergence in $W_2^2$ of a~difference solution of the {Dirichlet} problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {470--474},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a12/}
}
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G. K. Berikelashvili. The convergence in $W_2^2$ of a difference solution of the Dirichlet problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 470-474. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a12/