  A defect-deferred correction method, increasing both temporal and spatial
accuracy, for fluid-fluid interaction problem with nonlinear interface
condition is considered by geometric averaging of the previous two-time levels.
In the defect step, an artificial viscosity is added only on the fluctuations
in the velocity gradient by removing this effect on a coarse mesh. The
dissipative influence of the artificial viscosity is further eliminated in the
correction step while gaining additional temporal accuracy at the same time.
The stability and accuracy analyses of the resulting algorithm are investigated
both analytically and numerically.
