UFL Specification and User Manual 0.3 - FEniCS Project

UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Logg(v, w)(v, w, dm)where v and w are expressions of matching rank (so that inner(v, w) makessense), and dm is a measure. If the measure is left out, it is assumed that itis dx.The following example illustrates how to express a form containing integralsover subdomains and facets:a = (grad(v), grad(u)) + (v, b*grad(u), dx(2))+ (v, u, ds) + (jump(v), jump(u), dS)The following caveats should be noted:• The only operation allowed on a tuple is addition. In particular, tuplesmay not subtracted. Thus, a = (grad(v), grad(u)) - (v, u) mustbe expressed as a = (grad(v), grad(u)) + (-v, u).• Tuple notation may not be mixed with standard UFL integrand notation.Thus, a = (grad(v), grad(u)) + inner(v, u)*dx is notvalid.[Advanced] Tuple notation is strictly speaking not a part of the formlanguage, but tuples may be converted to UFL forms using the functiontuple2form available from the module ufl.algorithms. This is normallyhandled automatically by form compilers, but the tuple2form utility mayuseful when working with UFL from a Python script. Automatic conversionis also carried out by UFL form operators such as lhs and rhs.2.15 Form FilesUFL forms and elements can be collected in a form file with the extension.ufl. Form compilers will typically execute this file with the global UFL59