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A posteriori error estimation and adaptive strategy for the control of MsFEM computations

机译：MsFEM计算控制的后验误差估计和自适应策略

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摘要

We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaranteed and fully computable a posteriori error estimate for the global error measured in the energy norm. It is based on dual analysis and the Constitutive Relation Error (CRE) concept, with recovery of equilibrated fluxes from the approximate MsFEM solution. Second, the estimate is split into several indicators, associated to the various MsFEM error sources, in order to drive an adaptive procedure. The overall strategy thus enables to automatically identify an appropriate trade-off between accuracy and computational cost in the MsFEM numerical simulations. Furthermore, the strategy is compatible with the offline/online paradigm of MsFEM. The performances of our approach are demonstrated in several numerical experiments. (C) 2018 Elsevier B.V. All rights reserved.
机译：在使用多尺度有限元方法（MsFEM）进行的仿真中，我们引入了定量和鲁棒的工具来控制数值精度。首先，我们为能量范数中测得的整体误差提出了一个有保证且可完全计算的后验误差估计。它基于双重分析和本构关系误差（CRE）概念，可从近似MsFEM解决方案中恢复平衡通量。其次，将估计值分为几个指标，与各种MsFEM错误源相关联，以驱动自适应过程。因此，总体策略可以在MsFEM数值模拟中自动识别精度和计算成本之间的适当折衷。此外，该策略与MsFEM的脱机/在线模式兼容。我们的方法的性能在几个数值实验中得到了证明。 （C）2018 Elsevier B.V.保留所有权利。

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