What do u('+') and u('-') mean for a CR function u.

Question

Hello,

I define u = Function(FunctionSpace(mesh, 'CR', 1)) and then I would like to use the following bilinear form \int_{forall interior facet F} u(F)(jump terms)dS but there is an error message
because I should use the operators '+' and '-'.
What do u('+') and u('-') represent in this case? Are the values at the midpoint of the cell('+') and cell('-') respectively? Or is the value at the midpoint of F?

thank you in advance
Fotini

Answer 1

This has not much to do with midpoints. It is just notation to formally restrict a double-valued function u to either of the two elements ('+' and '-') sharing an internal facet. Note that there are also the abbreviations jump and average available which simplify the definition of such forms defined over non-conforming spaces.