[firedrake] 2D to 3D function

Dear all, First of all, thanks a lot for your time last Friday, and your help both for the implementation and for the installation of Firedrake. I am now trying to implement the equations we discussed on Friday, for the 3D potential flow equations. As a reminder, I solve the equations for phi, h, but also phi_s which is a 3D function, but is only updated at the free surface. However, I would like to update the interior nodes of phi_s as well, by copying the value of its surface nodes, as soon as they are updated (that is, simultaneously with solving the coupled equations). Is there a way to do this? I attach a short pdf summarising the equations, the current implementation and the issue I get. Thank you very much, Floriane