Hybridized CutFEM for Elliptic Interface Problems
This work provides a new numerical method for solving elliptic interface problems on unfitted meshes, which is important for computational mechanics and PDEs.
The authors develop a hybridized cut finite element method for elliptic interface problems, enabling coupling of general meshes over unfitted interfaces. They prove optimal error estimates and a condition number estimate for the Schur complement, with numerical examples confirming the theory.
We design and analyze a hybridized cut finite element method for elliptic interface problems. In this method very general meshes can be coupled over internal unfitted interfaces, through a skeletal variable, using a Nitsche type approach. We discuss how optimal error estimates for the method are obtained using the tools of cut finite element methods and prove a condition number estimate for the Schur complement. Finally, we present illustrating numerical examples.