# An unfitted Nitsche method for interface problems

**Sara Zahedi
**

Division of Scientific Computing

Department of Information Technology

Uppsala University

### Abstract:

I will present a finite element method for the Poisson equation and for the incompressible Stokes equations that allows for discontinuities along an interface not aligned with the mesh. The new method has, independently of the interface location, the following features:

- optimal-order accuracy for linear elements,

- the condition number of the system of equations is O(1/h2),

- the number of unknowns is fixed, and

- the method is easy to implement.

These properties are desirable in multiphase flow simulations, where both weak and strong discontinuities can be present. The method allows us to perform accurate multiphase flow simulations with standard linear elements without requiring the mesh to conform with the interfaces separating the immiscible fluids.