A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method
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有限元异构多尺度方法感兴趣量的后验误差估计
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
A. Nonnenmacher
中科院分区：
文献类型：
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作者：
A. Abdulle;A. Nonnenmacher
我们对通过有限元异质多尺度方法离散化的椭圆均质化问题的感兴趣量提出了“后验”误差分析。多尺度方法基于宏观到微观的公式，其中宏观物理问题在宏观有限元空间中离散化，并且使用相应微观问题的解来即时恢复丢失的宏观数据。我们提出了一个新的框架，允许在宏观层面遵循（单尺度）双加权残差方法的概念，以便导出多尺度问题的兴趣数量的后验误差估计。在宏观域中导出的局部误差指标可用于自适应目标导向的网格细化。这些误差指标仅依赖于可用的宏观和微观解决方案。我们进一步提供了数据近似误差的详细分析，包括正交误差。数值实验证实了自适应方法的效率以及我们对感兴趣数量的误差估计的有效性。 © 2013 Wiley periodicals, Inc. 数值方法偏微分方程，2013
We present an “a posteriori” error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro‐to‐micro formulation, where the macroscopic physical problem is discretized in a macroscopic finite element space, and the missing macroscopic data are recovered on‐the‐fly using the solutions of corresponding microscopic problems. We propose a new framework that allows to follow the concept of the (single‐scale) dual‐weighted residual method at the macroscopic level in order to derive a posteriori error estimates in quantities of interests for multiscale problems. Local error indicators, derived in the macroscopic domain, can be used for adaptive goal‐oriented mesh refinement. These error indicators rely only on available macroscopic and microscopic solutions. We further provide a detailed analysis of the data approximation error, including the quadrature errors. Numerical experiments confirm the efficiency of the adaptive method and the effectivity of our error estimates in the quantities of interest. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013