UFL Specification and User Manual 0.3 - FEniCS Project

UFL Specification and User Manual 0.3Martin S. Alnæs, Anders Loggthe facet (as seen from each of the two neighboring cells). If v is scalar, thenjump(v, n) is given byjump(v, n) ↔ v n = v + n + +v − n − . (2.46)If v is vector-valued, then jump(v, n) is given byjump(v, n) ↔ v n = v + ·n + +v − ·n − . (2.47)Thus, if the expression v is scalar, then jump(v, n) will be vector-valued,and if v is vector-valued, then jump(v, n) will be scalar.2.10.3 Average: avg(v)The operator avg may be used to express the average of an expression acrossa common facet of two cells:avg(v) ↔ 〈v〉 = 1 2 (v+ +v − ). (2.48)The expression avg(v) has the same value shape as the expression v.2.11 Conditional Operators2.11.1 ConditionalUFL has limited support for branching, but for some PDEs it is needed. Theexpression c inc = conditional(condition, true_value, false_value)evaluates to true value at run-time if condition evaluates to true, or tofalse value otherwise.ThiscorrespondstotheC++syntax(condition ? true value: false value),or the Python syntax (true value if condition else false value),48