Finite Elements Solutions of Boundary Value Problems Relevant to Geodesy

Abstract

The paper is aimed at a solution to the boundary value problem (BVP) with the Dirichlet and the Neumann boundary conditions by the finite element method (FEM). The computational domain for global gravity field modeling is 3D space above the Earth bounded by the Earth’s surface and upper spherical boundary. For local gravity field modeling on continental scale we choose only part of the Earth’s surface and create four additional side boundaries. On the Earth’s surface, the gravity disturbances generated from DNSC08 altimetry-derived data or EGM2008 geopotential model are considered. The disturbing potential on the upper spherical and side boundaries is generated from satellite model ITG-Grace. The derivation of FEM for this problem including the main discretization ideas is presented. Global quasigeoidal experiments and local refinements are performed. Later, solutions gained with linear and quadratic elements are compared and the influence of Dirichlet BC on the side boundaries on the local solution is studied. All numerical results are tested with potential generated from EGM2008 geopotential model.