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Weighted Estimate for the Convergence Rate of a Projection Difference Scheme for a Parabolic Equation and Its Application to the Approximation of the Initial-Data Control Problemстатья
Информация о цитировании статьи получена из
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Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
- Автор: Razgulin A.V.
- Журнал: Computational Mathematics and Mathematical Physics
- Том: 50
- Номер: 6
- Год издания: 2010
- Издательство: Pleiades Publishing, Ltd
- Местоположение издательства: Road Town, United Kingdom
- Первая страница: 969
- Последняя страница: 983
- DOI: 10.1134/S0965542510060059
- Аннотация: A new technique is proposed for analyzing the convergence of a projection difference scheme as applied to the initial value problem for a linear parabolic operator-differential equation. The technique is based on discrete analogues of weighted estimates reflecting the smoothing property of solutions to the differential problem for t > 0. Under certain conditions on the right-hand side, a new convergence rate estimate of order O(root tau + h) is obtained in a weighted energy norm without making any a priori assumptions on the additional smoothness of weak solutions. The technique leads to a natural projection difference approximation of the problem of controlling nonsmooth initial data. The convergence rate estimate obtained for the approximating control problems is of the same order O(root tau + h) as for the projection difference scheme.
- Добавил в систему: Разгулин Александр Витальевич