Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.

翻译：多尺度有限元方法（MsFEMs）现已成熟，是专门针对多尺度问题的有限元类方法。它们首先计算局部、振荡且依赖于问题的基函数，从而生成合适的离散空间，然后在该空间上对问题进行伽辽金近似。本文研究了如何以非侵入方式实现这些方法，以促进其在工业代码或非学术环境中的推广应用。我们构建了一个抽象框架，涵盖了针对线性二阶偏微分方程的多种MsFEMs。在该框架的完全一般性下发展了非侵入式MsFEM方法，这还有助于指导软件开发以及改进MsFEMs的理论理解与分析。