Zusammenfassung
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.
Nutzer