The finite element method as a tool to solve the oblique derivative boundary value problem in geodesy

Abstract

In this paper, we propose a novel approach to approximate
the solution of the Laplace equation with an oblique derivative
boundary condition by the finite element method.
We present and analyse diverse testing experiments to study
its behaviour and convergence. Finally, the usefulness of this
approach is demonstrated by using it to gravity field modelling,
namely, to approximate the solution of a geodetic boundary
value problem in Himalayas.