Singularity in gradient caused by Dirichlet boundary condition

I am looking for a mathematical explanation for the singularity caused by a Dirichlet boundary condition partially imposed at a boundary.

For instance
$$
nabla^2u=0 ~ text{in}~Omega
$$
where $Omega$ is a rectangle of 10 by 4. Dirichlet boundary condition $u=0$ is imposed at
$
y=0 ~text{and}~ y = 4 ~text{and}~ x < 2
$
and a flux is applied at the boundary $x=10$

Plotting the flux, you can see the singularity where the Dirichlet boundary condition ends

I plotted this with the following FEniCS code

from fenics import *

mesh = RectangleMesh(Point(0, 0), Point(10, 4), 400, 160, diagonal='crossed')

V = FunctionSpace(mesh, 'CG', 1)
u, v = TrialFunction(V), TestFunction(V)

a = inner(grad(u), grad(v))*dx


def MyDirichlet(x, on_boundary):
    return on_boundary and (x[0] < 2.0) and (x[0] > 0.0)

class MyNeumann(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary and near(x[0], 10.0)

subdomain = MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
subdomain.set_all(0)
myneumann = MyNeumann()
myneumann.mark(subdomain, 1)
ds = Measure('ds', domain=mesh, subdomain_data=subdomain)

bc = DirichletBC(V, Constant(0.0), MyDirichlet)

L = Constant(1.0)*v*ds(1)

u_sol = Function(V)

solve(a==L, u_sol, bcs=bc)
File("sing_example.pvd") << u_sol
Vflux = VectorFunctionSpace(mesh, 'CG', 1)
File("sing_flux.pvd") << project(grad(u_sol), Vflux)