UFL Specification and User Manual 0.3 - FEniCS Project

UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Logg2.10.1 Restriction: v(’+’) and v(’-’)When integrating over interior facets (*dS), one may restrict expressions tothe positive or negative side of the facet:element = FiniteElement("Discontinuous Lagrange","tetrahedron", 0)v = TestFunction(element)u = TrialFunction(element)f = Function(element)a = f(’+’)*dot(grad(v)(’+’), grad(u)(’-’))*dSRestriction may be applied to functions of any finite element space but willonly have effect when applied to expressions that are discontinuous acrossfacets.2.10.2 Jump: jump(v)The operator jump may be used to express the jump of a function across acommon facet of two cells. Two versions of the jump operator are provided.If called with only one argument, then the jump operator evaluates to thedifference between the restrictions of the given expression on the positive andnegative sides of the facet:jump(v) ↔ v = v + −v − . (2.45)If the expression v is scalar, then jump(v) will also be scalar, and if v isvector-valued, then jump(v) will also be vector-valued.Ifcalledwithtwoarguments,jump(v, n)evaluatestothejumpinvweightedby n. Typically, n will be chosen to represent the unit outward normal of47