DOLFIN User Manual - FEniCS Project

DOLFIN User ManualHoffman, Jansson, Logg, Wellsand the linear form L : ˆV → R is given by∫L(v) = v f dx. (2.6)Ω2.2.1 Setting up the variational problemThe variational problem (2.4) must be given to DOLFIN as a pair of bilinearand linear forms (a, L) using the form compiler FFC. This is done byentering the definition of the forms in a text file with extension .form, e.g.Poisson.form, as follows:element = FiniteElement(‘‘Lagrange’’, ‘‘triangle’’, 1)v = BasisFunction(element)U = BasisFunction(element)f = Function(element)a = dot(grad(v), grad(U))*dxL = v*f*dxThe example is given here for piecewise linear finite elements in two dimensions,but other choices are available, including arbitrary order Lagrangeelements in two and three dimensions.To compile the pair of forms (a, L), now call the form compiler on thecommand-line as follows:# ffc Poisson.formThis generates the file Poisson.h which implements the forms in C++ forinclusion in your DOLFIN program.17