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 L² 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.