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from dolfin import *
from IPython.display import Image


    

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mesh = UnitSquareMesh(6, 6)


    

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wiz = plot(mesh)
wiz.write_png("mesh")
Image("mesh.png")


    

    
Out[32]:

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


    

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u0 = Expression('1 + x[0]*x[0] + 2*x[1]*x[1]')


    

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def u0_boundary(x, on_boundary):
    return on_boundary


    

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bc = DirichletBC(V, u0, u0_boundary)


    

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u = TrialFunction(V)
v = TestFunction(V)


    

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f = Constant(50.0)
a = inner(nabla_grad(u), nabla_grad(v))*dx
L = f*v*dx


    

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


    

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# Plot solution and mesh
wiz = plot(u)
wiz.write_png("u")
Image("u.png")


    

    
Out[40]:

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dx?


    

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