I tried to implement the Stokes equation with purely Neumann boundary conditions. Since only Neumann conditions are applied, u is only determined up to a constant c. Then I added a Lagrange multiplier to the weak form so that the variational problem is well-posed.
k = 2
V = VectorH1(mesh,order=k)
Q = H1(mesh,order=k-1)
R = NumberSpace(mesh)
X = FESpace([V, Q, R, R])
gfu = GridFunction(X)
(u,p, lam1, lam2), (v,q, mu1, mu2) = X.TnT()
lam = CoefficientFunction((lam1, lam2))
mu = CoefficientFunction((mu1, mu2))[/code]
When running the code, the order of convergence of p was good, but the that of u was 0. The error of u is still the same when refining mesh. Please see the attached file.
Could you please tell me how to fix this error? Any help would be appreciated.
Thank you so much.