On the approximations of derivatives of integrated semigroups
On the approximations of derivatives of integrated semigroups
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DOI：
10.1515/jiip.2010.024
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发表时间：
2010
影响因子：
1.3
通讯作者：
Miao Li;V. Morozov;S. Piskarev
中科院分区：
文献类型：
--
作者：
Miao Li;V. Morozov;S. Piskarev
本文研究积分半群在时间变量上导数逼近过程中的正则化问题。我们考虑了直接法和基于A. N. Tikchonov的方法。证明了离散导数在一般Banach空间中的强收敛性，并得到了其收敛阶。在离散逼近格式的抽象框架下给出了介绍，离散逼近格式包括有限元法、有限差分法和投影法。
This paper is devoted to regularization in the process of derivative’s approximation of integrated semigroups in time variables. We consider the direct method and also the method based on A. N. Tikchonov’s approach. It is shown that discrete derivative converges in strong sense and the order of convergence in general Banach space is obtained. The presentation is given in the abstract framework of discrete approximation scheme, which includes finite element methods, finite difference schemes and projection methods.