Goal-oriented space-time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow
Goal-oriented space-time adaptivity in the finite element Galerkin method for the computation of nonstationary incompressible flow
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DOI：
10.1002/fld.2735
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发表时间：
2012-11-30
影响因子：
1.8
通讯作者：
Rannacher, Rolf
中科院分区：
文献类型：
--
作者：
Besier, Michael;Rannacher, Rolf
本文提出了一种设计非定常NavierStokes方程的自适应时空有限元离散的一般策略。其基本框架是面向目标的后验误差估计和自动网格自适应的双重加权残差法。在这种方法中，对某些物理兴趣量的近似误差，例如阻力系数，是根据计算解的局部残差乘以灵敏度因子来估计的，这些灵敏度因子是通过数值求解相关的对偶问题而获得的。在得到的局部误差指标中，空间和时间离散化的影响是分开的，这允许同时调整时间步长和空间网格大小。通过几个算例说明了该方法在经济网格构造和误差定量评估中的有效性。版权所有(C)2012 John Wiley&Sons，Ltd.
This paper presents a general strategy for designing adaptive spacetime finite element discretizations of the nonstationary NavierStokes equations. The underlying framework is that of the dual weighted residual method for goal-oriented a posteriori error estimation and automatic mesh adaptation. In this approach, the error in the approximation of certain quantities of physical interest, such as the drag coefficient, is estimated in terms of local residuals of the computed solution multiplied by sensitivity factors, which are obtained by numerically solving an associated dual problem. In the resulting local error indicators, the effects of spatial and temporal discretization are separated, which allows for the simultaneous adjustment of time step and spatial mesh size. The efficiency of the proposed method for the construction of economical meshes and the quantitative assessment of the error is illustrated by several test examples. Copyright (c) 2012 John Wiley & Sons, Ltd.