A DDFV-Based Approach to Oblique Derivative Boundary Value Problems with Applications in Geodesy

This poster presents a numerical scheme based on the Discrete Duality Finite Volume (DDFV) method for solving boundary value problems with oblique derivative boundary conditions. Such problems arise in various engineering applications where the boundary behavior of the solution is prescribed in a non-normal direction. The formulation of the boundary value problem and the proposed scheme are described, and the main theoretical properties of the method are discussed. The performance of the method is then investigated using two theoretical two-dimensional numerical experiments. In the first experiment, the oblique derivative vector is generated solely by translation, while in the second experiment it is generated by a combination of translation and rotation. These test cases are designed to verify the accuracy and reliability of the proposed numerical scheme. In the future, the method can be naturally extended to three-dimensional problems, making it particularly suitable for modeling the local and global Earth’s gravity field.