Global gravity field modelling by the finite element method involving mapped infinite elements.

Abstract

<p>We present a numerical approach for solving the oblique derivative boundary value problem (BVP) based on the finite element method (FEM) with mapped infinite elements. To that goal, we formulate the BVP consisting of the Laplace equation in 3D semi-infinite domain outside the Earth which is bounded by the approximation of the Earth's surface where the oblique derivative boundary condition is given. At infinity, regularity of the disturbing potential is prescribed. As the numerical method, we have implemented the FEM with mapped infinite elements, where the computational domain is divided into<br>two centrical parts, one meshed with finite elements and one with infinite ones. In numerical experiments, we firstly test a convergence of the proposed numerical scheme and then we deal with global gravity field modelling using EGM2008 data. To perform such numerical experiments, we create a special discretization of the Earth's surface to fulfil the conditions that arise from correct geometrical properties of finite elements. Then a reconstruction of EGM2008 aims to indicate efficiency of the presented numerical approach.</p>