ABSTRACT

In this talk, I will introduce Cut Finite Element Methods (CutFEM) for the Stokes interface problem and discuss recent developments, including stabilization techniques that preserve the incompressibility constraint within this class of unfitted finite element methods. Standard finite element methods require meshes that conform to complex geometries, which can be difficult and costly to generate. CutFEM offers an alternative by allowing interfaces and boundaries to intersect the computational mesh arbitrarily while retaining the accuracy and stability properties of conforming FEM. I will explain how CutFEM prevents ill-conditioning of the resulting linear systems and ensures stable, accurate discretizations on unfitted meshes. I will begin with stationary problems and then present our method for time-dependent PDEs in evolving domains.