## UC Berkeley / Lawrence Berkeley Laboratory

#### A uniformly well-conditioned, unfitted Nitsche method for interface problems

**Sara Zahedi, KTH, Stockholm**

##### May 4th, 2011 at 4PM–5PM in 939 Evans Hall [Map]

I will present a new finite element method for elliptic PDEs that allows for
discontinuities along an interface not aligned with the mesh. The main features
of the method are

- optimal-order accuracy for linear elements; we prove optimal orders in the
energy and
*L*² norms, and numerical experiments indicate optimal-order
pointwise errors,
- the condition number of the system of equations is O(1/h²),
independent of the interface location,
- the number of unknowns is fixed, independent of the location of the
interface, and
- the method is easy to implement.

These properties are desirable also for multiphase flow simulations, where
there can be a weak discontinuity in the velocity field and a discontinuity in
the pressure. I will also present an extension of the method to the stationary
incompressible Stokes equations with jump conditions for the normal stress at
the interface and numerically demonstrate optimal convergence order.