Solving the oblique derivative boundary-value problem by the finite volume method

Abstract

This paper deals with the oblique derivative boundary-value problem and its solution by the nite volume method. In this approach, the oblique derivative in the boundary condition is decomposed into this normal and tangential components which are then approximated by means of numerical solution values. The appropriate numerical schemes for 2D and 3D domains are developed and numerical experiments are performed. The numerical solutions are compared to the exact solutions and the second order accuracy of our 2D and 3D numerical scheme is obtained in all experiments. Our work is motivated by the large scale oblique derivative boundary value problem of physical geodesy.