Element boundary terms in reduced order models for flow problems: domain decomposition and adaptive coarse mesh hyper-reduction
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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.
CitationReyes, R.; Codina, R. Element boundary terms in reduced order models for flow problems: domain decomposition and adaptive coarse mesh hyper-reduction. "Computer methods in applied mechanics and engineering", Agost 2020, vol. 368, p. 113159:1-113159:27.