Goal-oriented error estimation and adaptivity for the finite element method
Goal-oriented error estimation and adaptivity for the finite element method
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DOI：
10.1016/s0898-1221(00)00317-5
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发表时间：
2001-03
影响因子：
2.9
通讯作者：
J. Oden;S. Prudhomme
中科院分区：
文献类型：
--
作者：
J. Oden;S. Prudhomme
在本文中，我们研究了一种后验误差估计的新方法，其中有限元近似的数值误差是根据感兴趣的数量而不是经典的能量范数来估计的。这些所谓的感兴趣量的特征是解所属函数空间上的线性泛函。我们在这里提出关于一类椭圆边值问题的理论，特别是展示如何获得准确的估计以及误差的上限和下限。我们还研究了面向目标的自适应性的新概念，它体现了旨在控制特定量误差的网格自适应程序。数值实验证实，与基于能量范数误差估计的传统自适应方案相比，这样的过程大大加速了解决方案局部特征达到预设精度的速度。
In this paper, we study a new approach in a posteriori error estimation, in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm. These so-called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs. We present here the theory with respect to a class of elliptic boundary-value problems, and in particular, show how to obtain accurate estimates as well as upper and lower bounds on the error. We also study the new concept of goal-oriented adaptivity, which embodies mesh adaptation procedures designed to control error in specific quantities. Numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates.