Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors
Adaptive finite element analysis of nonlinear problems: balancing of discretization and iteration errors
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DOI：
10.1515/jnum-2013-0002
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
R. Rannacher;Jevgeni Vihharev
中科院分区：
文献类型：
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作者：
R. Rannacher;Jevgeni Vihharev
摘要 本文继续作者之前的工作，对线性椭圆问题到非线性情况的有限元逼近中的离散化和迭代误差进行组合后验分析。底层理论框架同样是用于目标导向误差控制的双加权残差（DWR）方法。代数求解过程中的精度可以与使用可计算后验误差估计进行离散化的精度相平衡，其中外部非线性和内部线性迭代误差与离散化误差分离。这导致了代数迭代的有效停止标准，这是专门针对牛顿型方法而详细阐述的。针对几个非线性测试问题证明了所提出策略的性能。
Abstract This article continues prior work of the authors on the combined a posteriori analysis for the discretization and iteration errors in the finite element approximation of linear elliptic problems to the nonlinear case. The underlying theoretical framework is again that of the Dual Weighted Residual (DWR) method for goal-oriented error control. The accuracy in the algebraic solution process can be balanced with that due to discretization using computable a posteriori error estimates in which the outer nonlinear and inner linear iteration errors are separated from the discretization error. This results in effective stopping criteria for the algebraic iteration, which are elaborated particularly for Newton-type methods. The performance of the proposed strategies is demonstrated for several nonlinear test problems.