A Spectral element method to compute Earth's free core nutation

The Free Core Nutation (FCN) is a rotational mode caused by non-alignment of the rotation axis of the core and of the mantle. Its period observed by VLBI and superconducting gravimetry is around 430 sidereal days (Sd) with precision of better than 1 Sd, while its "theoretical" period calculated by traditional approaches and a given Earth model ranges from 450 to 470 Sd. Their gap of about 30 Sd is significant compared with its observation precision. We propose a spectral element method to compute the period of FCN and obtain a period of 434 Sd which is very close to the observed value.