A Solution for Local Gravity Field by Using Finite Element Method

According to the plane approximate expression of the geodetic boundary value problem,the formula for solving rocal gravity field by using the finite element method has been derived in this paper.And the three dimensions isoparametric finite element were applied to a topographical modle which consists of 121 nodes compased by grids with 100m×100m of each on the earth surface.The grids can also be arbitrary irregular quadrilaterals.The only needs of the modle are the gravity anomalies on the nodes.The mean square error of the results are m_ξ=±0.130" m_η=±0.144" m_ξ=±0.249×10^-4m and the CPU time(with Seiment 7570-C) was 8.15 seconds.This experiment shows that the finite element method can solve the boundary value problem of physical geodesy with advantage of being flexibler for setting up nodes and faster for computing than other methods.The method is suitable for an area around 100×100km²,but need 4 disturbing potentials or their derived quantities on the boundary outside the earth at lest.