Geodesic
Convergence of the projection-difference method for the approximate solution of a smoothly solvable parabolic equation with a weighted integral condition
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 2, Tome 176 (2020), pp. 61-69.

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We search for an approximate solution of an abstract linear parabolic equation in a Hilbert space with a nonlocal weighted integral condition by the projection-difference method and the implicit Euler method in time. The approximation of the problem with respect to spatial variables is oriented to the finite element method in the case of arbitrary projection subspaces under an additional smoothness condition. Estimates of errors of approximate solutions are established, the convergence of approximate solutions to the exact solution is proved, and the convergence rate is estimated.
Keywords: Hilbert space, nonlocal weighted integral condition, projection-difference method
Mots-clés : parabolic equation, implicit Euler method. 
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A. A. Petrova. Convergence of the projection-difference method for the approximate solution of a smoothly solvable parabolic equation with a weighted integral condition. 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 2, Tome 176 (2020), pp. 61-69. http://geodesic.mathdoc.fr/item/INTO_2020_176_a5/

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