I tried to enforce a zero-mean condition for a scalar GridFunction phi by directly subtracting its average:
Draw(phi)
mean_phi = Integrate(phi, mesh) / Integrate(1, mesh)
ones = phi.vec.CreateVector(); ones[:] = 1.0 # algebraic vector of ones
phi.vec.data -= mean_phi * ones
Draw(phi)
However, the result still looks offset, and a check like
print("mean after:", Integrate(phi, mesh))
does not reliably return a value close to zero. My understanding is that ones[:] = 1.0 only creates an algebraic vector of ones, which is not the same as the finite-element representation of the constant function 1. In other words, this operation is not mass-matrix consistent, so subtracting it does not actually remove the constant mode from phi.
My question is: if I do not want to use the Lagrange multiplier method, what is the correct way to enforce a zero-mean constraint in NGSolve? Should I construct the constant mode in a consistent way, for example by creating a GridFunction and setting it to 1:
const = GridFunction(phi.space); const.Set(1)
phi.vec.data -= (Integrate(phi, mesh) / Integrate(1, mesh)) * const.vec
or alternatively by computing the consistent constant vector ccc via solving M c = b with b_i = \int \varphi_i for each basis function, and then projecting with \phi \leftarrow \phi - (\int \phi)\, c? Is there perhaps a built-in projector in NGSolve that directly removes the mean with respect to the mass inner product? Another option I can think of is to pin a single scalar degree of freedom (fixing one pressure value) as a reference. Is that considered acceptable and stable, especially when using static condensation or HDG formulations?
Any advice or example code for a mass-matrix-consistent mean-removal approach would be greatly appreciated.