On the Convergence of the h-p Finite Element Method for Solving Boundary Value Problems in Physical Geodesy

A geopotential model of the Earth is usually calculated using the Stokes coefficients. As computational power has increased, research is focusing more on new ways of gravity field modelling. The objective of this work is to study an application of the h-p finite element method for solving boundary value problems in physical geodesy. For the purpose of studying this method, we have formulated model boundary value problems with different boundary conditions. The algorithm for solving these test problems was designed and was subsequently implemented by the program. We derived a weak formulation for each model boundary value problem and also the corresponding finite element discretization. We used isoparametric reference elements with linear and quadratic shape functions. The authors present the application of the h and p methodologies for increasing the rate of convergence of our solution, discuss mesh generation for large domains, and also solve the model boundary value problem, which is similar to the geodetic boundary value problem.