UFL Specification and User Manual 0.3 - FEniCS Project
UFL Specification and User Manual 0.3 - FEniCS Project
UFL Specification and User Manual 0.3 - FEniCS Project
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<strong>UFL</strong> <strong>Specification</strong> <strong>and</strong> <strong>User</strong> <strong>Manual</strong> <strong>0.3</strong>Martin S. Alnæs, Anders Logga = v*u*dxThis example is implemented in the file mass.ufl in the collection of demonstrationforms included with the <strong>UFL</strong> source distribution.3.2 Poisson’s equationThe bilinear <strong>and</strong> linear forms form for Poisson’s equation,∫a(v,u) = ∇v ·∇udx, (3.2)∫ΩL(v;f) = vf dx, (3.3)can be implemented as follows:Ωelement = FiniteElement("Lagrange", triangle, 1)v = TestFunction(element)u = TrialFunction(element)f = Function(element)a = dot(grad(v), grad(u))*dxL = v*f*dxAlternatively, index notation can be used to express the scalar product likethis:a = Dx(v, i)*Dx(u, i)*dxor like this:62
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