  In this work, we propose a numerical method based on high degree continuous
nodal elements for the Cahn-Hilliard evolution. The use of the p-version of the
finite element method proves to be very efficient and favorably compares with
other existing strategies (C^1 elements, adaptive mesh refinement, multigrid
resolution, etc). Beyond the classical benchmarks, a numerical study has been
carried out to investigate the influence of a polynomial approximation of the
logarithmic free energy and the bifurcations near the first eigenvalue of the
Laplace operator.
