On Adaptive Grad-Div Parameter Selection

We propose, analyze and test a new adaptive penalty scheme that picks the parameter $$\epsilon $$ element by small where $$\nabla \cdot u^h$$ is large. start analyzing testing on most simple but interesting setting, Stokes problem. Finally, we extend algorithm incompressible Navier equation complex flow problems. Tests indicate adaptive- method predicts behavior accurately. The developed in also can be used to pick grad-div stabilization parameter.