  A new method for interface tracking is presented. The interface
representation, based on domain decomposition, provides the interface location
explicitly, yet is Eulerian. This allows for well established finite difference
methods on uniform grids to be used for the numerics of advecting the interface
and other computations. CFL-stable and second order accurate explicit and
implicit time-stepping methods are derived. Numerical results are given to
substantiate stated convergence properties, as well as convergence in interface
curvature and mass conservation. Our method is applied to a boundary integral
formulation for Stokes flow, and the resulting integrals are analyzed and
treated numerically to second order accuracy. Finally, we embed our method in
the familiar immersed boundary- and immersed interface methods for two-phase
Navier-Stokes flow.
