Abstract In this paper we present a finite-element based reduced order model and, in particular, we consider two aspects related to the introduction of inter-element boundary terms in the formulation. The first is a domain decomposition strategy in which the transmission conditions involve boundary terms to account for non-matching meshes and discontinuous physical properties. The second is a coarse mesh hyper-reduction for which we propose an adaptive refinement driven by an a posteriori error estimator that contains element boundary terms. As the finite element full order model, the reduced order model is based on the Variational Multi-Scale framework, with sub-grid scales defined not only in the element interiors, but also on the inter-element boundaries. We present some examples of application using the incompressible Navier–Stokes equations and the Boussinesq approximation.

中文翻译：

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流动问题降阶模型中的元素边界项：域分解和自适应粗网格超约简

摘要 在本文中，我们提出了一个基于有限元的降阶模型，特别是，我们考虑了与在公式中引入元素间边界项相关的两个方面。第一个是域分解策略，其中传输条件涉及边界项以说明不匹配的网格和不连续的物理属性。第二个是粗网格超简化，我们提出了一种自适应细化，由包含元素边界项的后验误差估计器驱动。作为有限元全阶模型，降阶模型基于变分多尺度框架，子网格尺度不仅定义在单元内部，而且定义在单元间边界上。