Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: I. reduced formulation
Goal oriented adaptivity in the IRGNM for parameter identification in PDEs: I. reduced formulation
复制标题
DOI：
10.1088/0266-5611/30/4/045001
复制
发表时间：
2014-04-01
期刊：
影响因子：
2.1
通讯作者：
Veljovic, S.
中科院分区：
文献类型：
--
作者：
Kaltenbacher, B.;Kirchner, A.;Veljovic, S.
在本文中，我们研究了自适应离散的迭代正则化高斯-牛顿方法（IRGNM）与后验（差异原则）的正则化参数的选择，在每个牛顿步骤和停止指数。首先，我们证明了收敛性和收敛速度下的一些精度要求制定的四个数量的利益。然后讨论了基于加权对偶残差法的这些量的误差估计量的计算，从而得到一种自适应加细算法。最后，我们推广的结果，从Hilbert空间设置与二次罚款Banach空间和一般Tikhonov泛函的正则化的每一个牛顿步骤。
In this paper we study adaptive discretization of the iteratively regularized Gauss-Newton method (IRGNM) with an a posteriori (discrepancy principle) choice of the regularization parameter in each Newton step and of the stopping index. We first of all prove convergence and convergence rates under some accuracy requirements formulated in terms of four quantities of interest. Then computation of error estimators for these quantities based on a weighted dual residual method is discussed, which results in an algorithm for adaptive refinement. Finally we extend the results from the Hilbert space setting with quadratic penalty to Banach spaces and general Tikhonov functionals for the regularization of each Newton step.