On the Use of Galerkin’s Method in the Solution of the Geodetic Boundary Value Problem

Abstract

A generalized formulation of the geodetic boundary value problem and the concept of its weak solution were the starting point of this paper. The construction of a bilinear form connected with the problem in question was discussed and associated functional-analytic aspects reviewed. However, the main emphasis of the paper was on the interpretation of the above mentioned approach in terms of function bases. For this purpose the respective Galerkin’s system was constructed and a considerable attention was given to the computation of individual elements of Galerkin’s matrix and to an estimate of their accuracy. A majority of these problems were demonstrated for base functions given by elementary potentials of Laplace’s equation with a particular view to the influence of the topography of the boundary and the depth of individual mass concentrations.