An equation combines a list of operators into a scalar partial differential equation. Equations are used both for operators applied to the interior of a structure as well as for the aggregation of operators applied to a boundary or interface to enforce a boundary condition.
equation -solvesFor fieldName
-operators operatorList
[ -parabolic ]
[ -name equationName ]
The name of the equation is for debugging purposes. Any string may be used.
The fieldName being solved for specifies to which field nonlinear updates are applied. For parabolic systems of differential equations, this should be the field in the time derivative term.
Parabolic indicates that the PDE is of the form
where C is the fieldName being solved for. Instantaneous algebraic flux constraints, such as equations composed of a segregation operator are not parabolic.
If -parabolic is not specified, the equation is an elliptic PDE or a constraint equation of the form
and the nonlinear update is applied to the fieldName being solved for.