I have two question about solving an elliptic equation using multigrids.
First, in case of Neumann boundary conditions : Does the error equation, which is solved on the coarse grid, have the same boundary condition than the solution on the fine grid ? In the case of Dirichlet BC, since the value of the solution is known at the boundary exactly, the error is zero there, so I suppose the error equation for dirichlet BC always have homogeneous dirichlet BC (right ?) but what about neumann BCs ?
Second, what happens at the restriction/interpolation steps when I have a non constant coefficient in my differential operator ? Exemple : F(x) - n(xh)*d2F(x)/dx2 = S(x). Is the function n(x) restricted/interpolated the same way the solution F is?