The Q2-P1 element is one of the popular finite elements for incompressible flow problems in the mathematics community. For this element, the velocity field is approximated using bi-quadratic shape functions and the pressure field using linear shape functions. What makes this element pretty odd is the fact that the approximation for the pressure field is only linear but not bi-linear, i.e. the function space consists of $1, \xi_1$ and $\xi_2$ only but not the product term, $\xi_1 \, \xi_2$.
I have two questions on this element.
- Where are the pressure DOFs stored, if not at the nodes?
- What is the correct way of interpolating the pressure field for numerical integration and also for plotting?