On solving the nonlinear geodetic boundary value problem using mapped infinite elements

The numerical approach for solving the nonlinear geodetic boundary value problem based on the finite element method with mapped infinite elements and itterative procedure is developed and implemented. In this approach, the 3D semi-infinite domain outside the Earth is bounded only by the triangular discretization of the whole Earth's surface and extends to infinity. Then the BVP consists of the Laplace equation for unknown disturbing potential which holds in the domain, the nonlinear boundary condition given directly at computational nodes on the Earth's surface, and regularity of the disturbing potential at infinity. In experiments, a convergence of the proposed numerical scheme to the exact solution is tested and then the numerical study is focused on a reconstruction of the harmonic function above the Earth's topography.