A local quasigeoid determination by solving the nonlinear satellite-fixed geodetic boundary value problem

We present an iterative approach for solving the nonlinear satellite-fixed geodetic boundary value problem (NSFGBVP) by the finite element method that is applied for a determination of local quasigeoid in Himalayas and Andes. At first, we formulate the NSFGBVP that consists of the Laplace equation holding in the 3D bounded domain outside the Earth, the nonlinear boundary condition (BC) prescribed on the disretized Earth's surface, and the Dirichlet BC given on a spherical boundary placed approximately at the altitude of chosen satellite mission and additional four side boundaries. Then the iterative approach is based on determining the direction of actual gravity vector together with the value of the disturbing potential. Such a concept leads to the first iteration where the oblique derivative boundary value problem is solved, and the last iteration represents the approximation of the actual disturbing potential and the direction of gravity vector. As a numerical method for our approach, we have implemented the finite element method with triangular prisms. Finally, we present a high-resolution numerical experiment dealing with the local gravity field modelling in Himalayas and Andes.