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Holota, Petr ; Nesvadba, Otakar

**Annotation: **The motivation comes from the role of boundary value problems in Earth?s gravity field studies. The focus is on Neumann?s problem in the exterior of an oblate ellipsoid of revolution. The approach follows the concept of variational methods and the notionof the weak solution. The solution of the problem is approximated by linear combinations of basis functions with scalar coefficients, i.e. by Galerkin approximations. The aim is to discuss the construction of Galerkin?s matrix for elementary potentialsused in quality of a function basis. The computation of the entries of Galerkin?s matrix is expected to be simple for the elementary functions like these. Nevertheless, the opposite is true. Ellipsoidal harmonics are applied as a natural tool. The problem, however, is the summation of the series that represent the entries. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics.

**Citation: **HOLOTA, Petr a Otakar NESVADBA. On the construction of Galerkin?s matrix for elementary potentials in case of an ellipsoidal solution domain in Earth?s gravity field studies [online]. In: . Bratislava: Slovak University of Technology, 2015 [cit. 2019-01-09].

**Publication type: **audiovizuální tvorba

*The record appears in these collections:*

Focus on VÚGTK > VÚGTK Departments > Geodesy and Geodynamics

Focus on VÚGTK > Staff VÚGTK > Otakar Nesvadba

Focus on VÚGTK > Staff VÚGTK > Petr Holota

Documents of VÚGTK > Grey literature VÚGTK

Focus on VÚGTK > RIV

Record created 2018-11-15, last modified 2019-04-26