Help in the implementation of a mixed displacement-pressure formulation

Hello everybody,

I'm a PhD student and as part of my research I need to implement a triangular finite element using the displacement/pressure mixed formulation. I'm implementing two field incompressible elasticity from the book of Zienkiewicz and Taylor "The finite element method, Vol. I". The mixed approximation form is given as:

|A*u + C*p = f1
|
|C^T*u - V*p = 0

which leads to (A + C*V^-1*C^T)*u=f1.

The matrix V is given by integral((Np^T*Np)/K), with Np=[N1 N2 N2], where Ni are the shape functions and K the bulk modulus. (^T) is the transpose operator and (^-1) the inverse.

 By multiplying Np^T*Np, the resulting matrix will have linearly dependent lines. Therefore, matrix V cannot be inverted and the mixed formulation isn't correctly applied.

Am I missing some step in the procedure? How can I implement the mixed formulation correctly?

Thanks in advance,
jfmc