  We consider a saddle point formulation for a sixth order partial differential
equation and its finite element approximation, for two sets of boundary
conditions. We follow the Ciarlet-Raviart formulation for the biharmonic
problem to formulate our saddle point problem and the finite element method.
The new formulation allows us to use the $H^1$-conforming Lagrange finite
element spaces to approximate the solution. We prove a priori error estimates
for our approach. Numerical results are presented for linear and quadratic
finite element methods.
