An H^1-Galerkin mixed finite element method is applied to the extended Fisher-Kolmogorov equation by employing a splitting technique. The method described in this paper
may also be considered as a Petrov-Galerkin method with cubic spline space as trial space and
piecewise linear space as test space, since second derivative of a cubic spline is a linear spline.
Optimal order error estimates are obtained without any restriction on the mesh. Fully discrete
scheme is also discussed and optimal order estimates are obtained. The results are validated with