[firedrake] Solve a Variational problem in a part of the domain

[Anna Kalogirou]

Dear all,

I have a rather simple question but I would like to get some feedback from someone in the Firedrake team. 

I am now working on the problem which includes solving a variational problem in a part of the domain only (a water wave problem which includes a floating body). 

I can think of a couple of possible solutions on how to solve this:
1. Define two domains and solve the problem separately in each domain. However, I will have to deal with nonzero boundary conditions on the common boundary.

2. I prefer solving the problem in the whole domain, since most of the equations/functions are valid everywhere. Then I can define a Heavyside step function which will be 0 in one part and 1 in the part of the domain I am interested in (under the floating body). I will essentially write down a variational problem valid everywhere, but will actually be zero in a part of the domain.

Is the 2nd step a good approach? The question essentially is how to split a mass matrix M_kl which is defined everywhere, and solve and integral form in a part of the domain only. 

Thank you.

Regards,

Anna.