Michael,
I'm sorry for taking so long to reply. You may have already found a 
solution to your problem, or...

> velocity = (last velocity) + (projected acceleration due to external
> forces) + constant * pressure.
>
> This relationship is obtained from a simplification of the mechanical
> boundary condition and applying this expression can hopefully
> stabilize the system. The expression is of the form: V = k1 + k2 * P.
> I see that the constraints matrix class can handle linear homogeneous
> constraints on the degree of freedom. Is it easy to extend this class
> to handle the case above?

...you may wish to check out the extensions that Martin Kronbichler has 
written for the ConstraintMatrix class that can now also handle 
inhomogenous constraints like the ones you need.

The class is in the subversion repository from which you can check it out. 
Alternatively, it will also be in the upcoming release which I hope we'll 
get out the door in the next couple of weeks or so.

Best
 Wolfgang

-- 
-------------------------------------------------------------------------
Wolfgang Bangerth                email:            [email protected]
                                 www: http://www.math.tamu.edu/~bangerth/

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