UFL Specification and User Manual 0.3 - FEniCS Project

UFL Specification and User Manual 0.3Martin S. Alnæs, Anders LoggThe corresponding finite element variational problem for discontinuous firstorder elements may be implemented as follows:cell = triangleDG1 = FiniteElement("Discontinuous Lagrange", cell, 1)v = TestFunction(DG1)u = TrialFunction(DG1)f = Function(DG1)g = Function(DG1)#h = MeshSize(cell) # TODO: Do we include MeshSize in UFL?h = Constant(cell)alpha = 1 # TODO: Set to proper valuegamma = 1 # TODO: Set to proper valuea = dot(grad(v), grad(u))*dx \- dot(avg(grad(v)), jump(u))*dS \- dot(jump(v), avg(grad(u)))*dS \+ alpha/h(’+’)*dot(jump(v), jump(u))*dS \- dot(grad(v), jump(u))*ds \- dot(jump(v), grad(u))*ds \+ gamma/h*v*u*dsL = v*f*dx + v*g*dsThis example is implemented in the file poisson dg.ufl in the collection ofdemonstration forms included with the UFL source distribution.3.10 Quadrature elementsFIXME: The code examples in this section have been mostly converted toUFL syntax, but the quadrature elements need some more updating, as wellas the text. In UFL, I think we should define the element order and not the70