Spherical Harmonic Finite Approximation Method for the Stokes-NeummanMixed Boundary Value Problem with a Sphere Cap

A method solving the Stokes-Neumman Mixed Boundary Value Problem(S-N MBVP)witha sphere cap is studied in this paper.First,we discuss the method for S-N MBVP with the polar cap.Then S-N MBVP with general sphere cap is solved with the help of coordinate transformation.Thetransformation between spherical coefficients in different coordinate systems is also studied.By mak-ing use of the imitation computation for the EGM08model,it is concluded that the solution methodgiven in the paper can be accurate to submillimeter level.S-N MBVP can be used to refine the localgeoid,our results show the recovered height of a geoid in the interior of the spherical cap can reach tothe accuracy of 5centimeters.Our results show that the proposed method not only is effective in theo-ry,but also has sufficient precision to deal with many kinds of gravity data.