it happened for me to need to evaluate the "volume" of Face elements in my code through these functions:

Real Tri3::volume () const

Real Quad4::volume () const

...however, i noticed that the same function is not implemented for Tri6, Quad8, Quad9 and so on... due to the fact that these elements might have curved shaped, therefore none can use an analytic expression to evaluate their "volume".

my question: do you think that it would fine in the next version of libMesh to calculate the "volume" through standard Gauss integration:

Vol = sum_{i=0}^{nqp}{ JxW[i] }

i think that this might work for a decent number of quadrature points. obviously the same rule can be applied for 3D quadratic elements and for the high-order 1D elements too.

cheers,

Vas