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Gravity field modelling by the FEM and FVM using the second derivatives of disturbing potential as the boundary condition

Authors

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

Minarechová,  Zuzana
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;

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

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

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Citation

Macák, M., Minarechová, Z., Mikula, K., Čunderlík, R., Tomek, L. (2023): Gravity field modelling by the FEM and FVM using the second derivatives of disturbing potential as the boundary condition, XXVIII General Assembly of the International Union of Geodesy and Geophysics (IUGG) (Berlin 2023).
https://doi.org/10.57757/IUGG23-3826


Cite as: https://gfzpublic.gfz-potsdam.de/pubman/item/item_5020719
Abstract
We present global gravity field modelling by the finite element and finite volume methods where the second derivatives of disturbing potential are taken into account directly as the boundary condition. To that goal, we define the 3D finite computational domain bounded from the bottom by the Earth's surface and from the top by an artificial boundary at the level of GOCE satellites. Then the boundary value problem consists of the Laplace equation accompanied by the first derivatives of disturbing potential given on the bottom boundary and the second derivatives of the disturbing potential given on the upper boundary. To solve such a problem, we apply the finite element as well as the finite volume methods to obtain the corresponding numerical schemes. Finally, we study and test the order of convergence of these schemes by theoretical numerical experiments, and then we focus on global gravity field modelling.