481 RWTH Publication No: 730319        2018        IGPM481.pdf
TITLE A multigrid method for unfitted finite element discretizations of elliptic interface problems
AUTHORS Thomas Ludescher, Sven Groß, Arnold Reusken
ABSTRACT We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three methods rely on Nitsche’s method to incorporate the interface conditions. The main topic of the paper is the development of a multigrid method, based on a novel prolongation operator for the unfitted finite element space and an interface smoother that is designed to yield robustness for large jumps in the diffusion coefficients. Numerical results are presented which illustrate efficiency of this multigrid method and demonstrate its robustness properties with respect to variation of the mesh size, location of the interface and contrast in the diffusion coefficients.
KEYWORDS geometric multigrid, unfitted finite elements, interface problem, Nitsche, CutFEM
DOI 10.1137/18M1203353
PUBLICATION SIAM Journal on Scientific Computing
42(1), pp A318–A342