An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems
An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems
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DOI：
10.1002/nme.5440
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发表时间：
2017-06
影响因子：
2.9
通讯作者：
M. Iqbal;H. Gimperlein;M. S. Mohamed;O. Laghrouche
中科院分区：
文献类型：
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作者：
M. Iqbal;H. Gimperlein;M. S. Mohamed;O. Laghrouche
我们提出研究传热问题的时间相关广义有限元模拟的后验误差估计。残差估计可以为数值误差提供可靠且实用的上限，而与启发式选择的富集函数无关。提出了两组数值实验。首先，随着丰富函数数量的增加或时间离散化的细化，误差估计显示出误差的减少。其次，该估计用于在没有精确解可用的情况下预测误差的行为。它还反映了在广义有限元方法中通常遇到的不良条件系统中产生的误差。最后，我们研究各个时间步长和网格元素中的局部误差指标。这为富集函数的自适应选择和细化奠定了基础。版权所有 © 2016 约翰·威利父子有限公司
We propose the study of a posteriori error estimates for time‐dependent generalized finite element simulations of heat transfer problems. A residual estimate is shown to provide reliable and practically useful upper bounds for the numerical errors, independent of the heuristically chosen enrichment functions. Two sets of numerical experiments are presented. First, the error estimate is shown to capture the decrease in the error as the number of enrichment functions is increased or the time discretization refined. Second, the estimate is used to predict the behaviour of the error where no exact solution is available. It also reflects the errors incurred in the poorly conditioned systems typically encountered in generalized finite element methods. Finally, we study local error indicators in individual time steps and elements of the mesh. This creates a basis towards the adaptive selection and refinement of the enrichment functions. Copyright © 2016 John Wiley & Sons, Ltd.