Crouzeix-Raviart MsFEM with Bubble Functions for Diffusion and Advection-Diffusion in Perforated Media (Communications in Computational Physics, 2018)
The adaptation of Crouzeix-Raviart finite element in the context of multiscalefinite element method (MsFEM) is studied and implemented on diffusion andadvection-diffusion problems in perforated media. It is known that the approximationof boundary condition on coarse element edges when computing the multiscale basisfunctions critically influences the eventual accuracy of any MsFEM approaches. Theweakly enforced continuity of Crouzeix-Raviart function space across element edgesleads to a natural boundary condition for the multiscale basis functions which relaxesthe sensitivity of our method to complex patterns of perforations. Another ingredientto our method is the application of bubble functions which is shown to be instrumentalin maintaining high accuracy amid dense perforations. Additionally, the applicationof penalization method makes it possible to avoid complex unstructured domain andallows extensive use of simpler Cartesian meshes.