Returning a solution at any point on the domain

General
1

I have code to solve over a dense mesh. Once I have the solution I want to be able to query the solution gfu at an arbitrary point in the domain. Not only on the mesh vertices which is what I can do now. How would I do this? Thank you for your time

def solve_FEM(ref_mesh):
# H1-conforming finite element space
fes = H1(ref_mesh, order=1, dirichlet=“bottom”, autoupdate=True)
# define trial- and test-functions
u = fes.TrialFunction()
v = fes.TestFunction()

# the bilinear-form
a = BilinearForm(grad(u)*grad(v)*dx)

funcf = 1*x*y
f = LinearForm(funcf*v*dx)

a.Assemble()
f.Assemble()
# Draw(funcf,mesh)
gfu = GridFunction(fes)
gfu.vec.data = a.mat.Inverse(freedofs=fes.FreeDofs()) * f.vec
return gfu, fes
2 
gfu(mesh(0.1,0.1.0, 0.1))

best