We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the MsFEM framework, the concept of Constitutive Relation Error (CRE) to obtain a guaranteed and fully computable a posteriori error estimate in the energy norm (as well as error indicators on various error sources). Here, the CRE concept is coupled with the solution of an adjoint problem to control the error and drive an adaptive procedure with respect to a given output of interest. Furthermore, a local and non-intrusive enrichment technique is proposed to enhance the accuracy of error bounds. The overall strategy, which is fully automatic and robust, enables to reach an appropriate trade-off between certified reliability and computational cost in the MsFEM context. The performances of the proposed method are investigated on several illustrative numerical test cases. In particular, the error estimation is observed to be very accurate, yielding a very efficient adaptive procedure.

我们介绍了使用多尺度有限元方法（MsFEM）进行多尺度计算的面向目标的策略。在先前的工作中，我们展示了如何在MsFEM框架中使用本构关系错误（CRE）概念来获得有保证且可完全计算的后验能源规范中的误差估计（以及各种误差源上的误差指示符）。这里，CRE概念与伴随问题的解决方案相结合，以控制错误并针对给定的目标输出驱动自适应过程。此外，提出了一种局部和非侵入式的富集技术，以提高误差范围的准确性。完全自动化且强大的总体策略可以在MsFEM上下文中在认证的可靠性和计算成本之间达成适当的折衷。在几个示例性的数值测试案例上研究了该方法的性能。特别地，观察到误差估计非常准确，从而产生了非常有效的自适应过程。