from dolfin import *

f = Expression ( "pow ( x[0] - 1, 2 ) + pow ( x[1], 2 ) - 1.0" )
bc_fun = Expression ( "0.0" )

center = Point ( 1.0, 0.0 )
mesh = CircleMesh ( center, 1.0, 0.25 );

V = FunctionSpace ( mesh, 'Lagrange', 1 )

def boundary ( x, on_boundary ):
  return on_boundary

bc = DirichletBC ( V, bc_fun, boundary )
#
#  Define the variational problem
#
u = TrialFunction ( V )
v = TestFunction ( V )
A = inner ( grad ( u ), grad ( v ) ) * dx
RHS = f * v * dx
w = Function ( V )
#
#  Solve.
#
solve ( A == RHS, w, bc )

plot ( w, title = "Solution" )

plot ( mesh, title = "Mesh" )

file = File ( 'circle.xml' )
file << mesh

interactive ( )