Multiscale Finite Element methods for advection-dominated problems in perforated domains
For researchers in computational mechanics, this is an incremental extension of prior work to advection-dominated problems in perforated domains.
The paper investigates multiscale finite element methods for advection-dominated diffusion in perforated domains, comparing variants based on weak continuity conditions and stabilized formulations. No concrete numerical results are provided.
We consider an advection-diffusion equation that is advection-dominated and posed on a perforated domain. On the boundary of the perforations, we set either homogeneous Dirichlet or homogeneous Neumann conditions. The purpose of this work is to investigate the behavior of several variants of Multiscale Finite Element type methods, all of them based upon local functions satisfying weak continuity conditions in the Crouzeix-Raviart sense on the boundary of mesh elements. In the spirit of our previous works [Le Bris, Legoll and Lozinski, CAM 2013 and MMS 2014] introducing such multiscale basis functions, and of [Le Bris, Legoll and Madiot, M2AN 2017] assessing their interest for advection-diffusion problems, we present, study and compare various options in terms of choice of basis elements, adjunction of bubble functions and stabilized formulations.