Implementing weak constraints

Hello,

I am trying to implement weak constraints on my boundary using a model coupling integration variable. The idea is that flow at the boundary is determined by change in the area at that time. Here are my specific questions:

(1) How do you implement constraints on a primary dependent variable? Whats the mathematical procedure you adopt to maintain the constraint?
(2) Do you use penalty or Augmented Lagrange method?
(3) If it is some thing else, how do you give it in COMSOL?
(4) What caveats should we look for and how do we be careful?

Thanks!
Padmini