__author__ = "Anders Logg <logg@simula.no>"
__date__ = "2012-01-19"
__copyright__ = "Copyright (C) 2012 Anders Logg"
__license__  = "GNU LGPL version 3 or any later version"

# Last changed: 2012-01-19

from dolfin import *

# Create mesh and define function space
mesh = UnitSquare(32, 32)
V = FunctionSpace(mesh, "Lagrange", 1)

# Define Dirichlet boundary (x = 0 or x = 1)
def boundary(x, on_boundary):
    return on_boundary

# Define boundary condition
u0 = Constant(0.0)
bc = DirichletBC(V, u0, boundary)

# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Expression("2.0*DOLFIN_PI*DOLFIN_PI*sin(DOLFIN_PI*x[0])*sin(DOLFIN_PI*x[1])")
a = inner(grad(u), grad(v))*dx
L = f*v*dx

# Compute solution
u = Function(V)
solve(a == L, u, bc)

# Save solution in VTK format
file = File("poisson.pvd")
file << u

# Plot solution
plot(u, interactive=True)