Geodesic
Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 129-139

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Application of the Galerkin methods to the numerical analysis of the integro-differential electric field equation is justified. The convergence of the Galerkin methods is established for a class of equations with nonelliptic operators comprising the electric field equation. Theorems concerning the approximation of the elements belonging to a special Sobolev space by the basis Rao–Wilton–Glisson functions are proved. The rate of convergence is estimated. 
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     author = {Yu. G. Smirnov},
     title = {Convergence of the {Galerkin} methods for equations with elliptic operators on subspaces and solving the electric field equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {129--139},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a12/}
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Yu. G. Smirnov. Convergence of the Galerkin methods for equations with elliptic operators on subspaces and solving the electric field equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a12/