Geodesic
Error estimates for the Galerkin method as applied to time-dependent equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1643-1651

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A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives are obtained. The method is applied to initial-boundary value problems for parabolic equations. 
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     author = {P. V. Vinogradova and A. G. Zarubin},
     title = {Error estimates for the {Galerkin} method as applied to time-dependent equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1643--1651},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a10/}
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P. V. Vinogradova; A. G. Zarubin. Error estimates for the Galerkin method as applied to time-dependent equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1643-1651. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a10/