Finite element discretization of the governing equations

The required working equations are derived by application of the following finite element schemes to the described governing model  

Standard Galerkin procedure - to discretize the circumferential component of the equation of motion, Equation (5.23), for the calculation of vs. 

Continuous penalty method - to discretize the continuity and (r, z) components of the equation of motion, Equations (5.22) and (5.24), for the calculation of r,. and v. Pressure is computed via the variational recovery procedure (Chapter 3, Section 4). 

Elemental stiffness equations (i.e. the working equations) resulting from the described discredzations are in general written as 

---