UFL Specification and User Manual 0.3 - FEniCS Project

UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Loggf = Function(element)Note that the order in which Functions are declared is important, directlyreflected in the ordering they have among the arguments to each Form theyare part of.Function is used to represent user-defined functions, including, e.g., sourceterms, body forces, variable coefficients and stabilization terms. UFL treatseach Function as a linear combination of unknown basis functions with unknowncoefficients, that is, UFL knows nothing about the concrete basisfunctions of the element and nothing about the value of the function.Note that more than one function can be declared for the same FiniteElement.ThefollowingexampledeclarestwoBasisFunctionsandtwoFunctionsfor the same FiniteElement:v = BasisFunction(element)u = BasisFunction(element)f = Function(element)g = Function(element)For a Function on a MixedElement (or VectorElement or TensorElement),the function split can be used to extract function values on subspaces, asillustrated here for a mixed Taylor–Hood element:up = Function(TH)u, p = split(up)A shorthand for this is in place called Functions:u, p = Function(TH)26