On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients
On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients
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DOI：
10.1137/s1064827501383713
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发表时间：
2002-10-31
影响因子：
3.1
通讯作者：
Dai, SB
中科院分区：
文献类型：
--
作者：
Chen, ZM;Dai, SB
基于后验误差估计的自适应有限元方法的成功实施取决于几个因素：后验误差指示器、精化/粗化策略以及各种参数的选择。本文的目的是考察这些因素对具有强间断系数的线性椭圆型方程模型问题的自适应有限元方法性能的影响。我们推导了一个新的后验误差估计，它局部依赖于奇点附近系数的振荡。大量的数值实验支持了我们的理论结果，并展示了所提出的自适应算法的竞争行为。
The successful implementation of adaptive finite element methods based on a posteriori error estimates depends on several ingredients: an a posteriori error indicator, a refinement/coarsening strategy, and the choice of various parameters. The objective of the paper is to examine the influence of these factors on the performance of adaptive finite element methods for a model problem: the linear elliptic equation with strongly discontinuous coefficients. We derive a new a posteriori error estimator which depends locally on the oscillations of the coefficients around singular points. Extensive numerical experiments are reported to support our theoretical results and to show the competitive behaviors of the proposed adaptive algorithm.