TY - JOUR
T1 - Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media
AU - Pierre Degond, Alexei Lozinski, Bagus Putra Muljadi & Jacek Narski
JO - Communications in Computational Physics
VL - 4
SP - 887
EP - 907
PY - 2018
DA - 2018/04
SN - 17
DO - http://doi.org/10.4208/cicp.2014.m299
UR - https://global-sci.org/intro/article_detail/cicp/10982.html
KW - 
AB - <p style="text-align: justify;">The adaptation of Crouzeix-Raviart finite element in the context of multiscale
finite element method (MsFEM) is studied and implemented on diffusion and
advection-diffusion problems in perforated media. It is known that the approximation
of boundary condition on coarse element edges when computing the multiscale basis
functions critically influences the eventual accuracy of any MsFEM approaches. The
weakly enforced continuity of Crouzeix-Raviart function space across element edges
leads to a natural boundary condition for the multiscale basis functions which relaxes
the sensitivity of our method to complex patterns of perforations. Another ingredient
to our method is the application of bubble functions which is shown to be instrumental
in maintaining high accuracy amid dense perforations. Additionally, the application
of penalization method makes it possible to avoid complex unstructured domain and
allows extensive use of simpler Cartesian meshes.</p>