Geodesic
Root mean square error estimates for the projection-difference method for the approximate solution of a parabolic equation with a periodic condition for the solution
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 118-123.

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We construct an approximate solution of an abstract linear parabolic equation in a separable Hilbert space with a periodic condition for a solution by the projection-difference method. We use the Galerkin method for the spatial variables and the implicit Euler discretization for time. We obtain root mean square estimates of the error of approximate solutions that are effective both in time and spatial variables; these estimates imply the convergence of approximate solutions to an exact solution and allow one to find the convergence rate.
Keywords: Hilbert space, periodic condition, projection-difference method, root mean square error estimate.
Mots-clés : parabolic equation 
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     author = {A. S. Bondarev},
     title = {Root mean square error estimates for the projection-difference method for the approximate solution of a parabolic equation with a periodic condition for the solution},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {118--123},
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     volume = {175},
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A. S. Bondarev. Root mean square error estimates for the projection-difference method for the approximate solution of a parabolic equation with a periodic condition for the solution. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 118-123. http://geodesic.mathdoc.fr/item/INTO_2020_175_a9/

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