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Solving the oblique derivative boundary value problems by the infinite element method

Authors

Minarechova,  Zuzana
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Macák,  Marek
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Čunderlík,  Róbert
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

Mikula,  Karol
IUGG 2023, General Assemblies, 1 General, International Union of Geodesy and Geophysics (IUGG), External Organizations;

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Citation

Minarechova, Z., Macák, M., Čunderlík, R., Mikula, K. (2023): Solving the oblique derivative boundary value problems by the infinite element method, XXVIII General Assembly of the International Union of Geodesy and Geophysics (IUGG) (Berlin 2023).
https://doi.org/10.57757/IUGG23-3829


Cite as: https://gfzpublic.gfz-potsdam.de/pubman/item/item_5020716
Abstract
We formulate the boundary value problem in 3D semi-infinite domain outside the Earth, which consists of the Laplace equation for unknown disturbing potential, the oblique derivative boundary condition prescribed on the Earth’s surface, and the regularity of the disturbing potential at infinity. As a numerical method for our approach, we derive the numerical scheme based on the finite element method with mapped infinite elements. In this way, the regularity condition is taken into account naturally. Then to perform the numerical experiments, we create a special discretization of the Earth's surface which fulfils the conditions that arise from the correct geometrical properties of the finite elements. Finally, we present the numerical experiments, where we test the proposed numerical scheme, and then we focus on gravity field modelling.