Augmented Lagrange multiplier method

Question

Hi all,

I would like to implement an augmented Lagrangian method for quasi incompressibility. This include the augmentation of a Lagrange mutiplier $ \lambda $ and a constraint function $h(\theta)$ i.e.,

$$W(u,\theta,p) + \int_{\Omega} \lambda h(\theta) dV $$

The Lagrange multiplier gets updated $ \lambda_{k+1} = \lambda_{k} + \epsilon h(\theta)$ after each Newton Solve.

I was wondering is there anyway to have $ \lambda$ as a field variable in FeNiCs that I can modify after each Newton solve?

Thanks!