  The defining equations for Killing vector fields and conformal Killing vector
fields are overdetermined systems of PDE. This makes it difficult to solve the
systems numerically. We propose an approach which reduces the computation to
the solution of a symmetric eigenvalue problem. The eigenvalue problem is then
solved by finite element techniques. The formulation itself is valid in any
dimension and for arbitrary compact Riemannian manifolds. The numerical results
which validate the method are given in two dimensional case.
