On Finite Element and Finite Volume Methods and Their Application in Regional Gravity Field Modeling

Abstract

The article is focused on a solution to the geodetic boundary value problem (GBVP) by new numerical approaches, namely the finite element (FEM) and finite volume (FVM) methods. In spite of previous numerical approaches (like BEM or FFT), where the solution was sought on Earth's surface or its approximation, our numerical solution is computed in 3D computational domain above the Earth bounded by the chosen part of the Earth's surface - area of Slovakia, corresponding upper spherical artificial boundary and four other planar boundaries. On the upper spherical and planar boundaries the Dirichlet boundary condition (BC) are generated from EGM96 geopotential model. On the Earth's surface, discretized by series of triangles, we consider the surface gravity disturbances as the Neumann BC. They are obtained from discrete terrestrial gravimetric measurements. The disturbing potential as a direct numerical result is transformed to quasigeoidal heights. © Springer-Verlag Berlin Heidelberg 2010.