how to get a FunctionSpace with a zero mean value in global domain in firedrake?

[tu1620808124]

I have seen a problem(sometimes Poisson equation) with a condition having zero mean value in the domain just like:

I want to know if there's a way to get this function space in firedrake, more detail can be seen in the reference:

Masud A, Hughes T J R. A stabilized mixed finite element method for Darcy flow[J]. Computer methods in applied mechanics and engineering, 2002, 191(39-40): 4341-4370.

[dham]

You can't make this function space (or its subspaces) directly in Firedrake, but there are two ways of working with constrained function spaces when you actually need to solve problems. The first is to introduce a Lagrange multiplier imposing the zero integral constraint. This is documented here. This directly imposes the constraint, but at the cost of making your variational problem harder to solve. The approach that is usually preferred is to specify your solution in the unconstrained space and to tell the solver about the resulting nullspace in the differential operator. This is covered here.