000193616 001__ 193616 000193616 003__ CZ-ZdVUG 000193616 005__ 20190201124455.0 000193616 040__ $$aABC039$$bcze 000193616 1001_ $$aHolota, Petr 000193616 24510 $$aFundamental solution of Laplace?s equation in oblate spheroidal coordinates and Galerkin?s matrix for Neumann?s problem in Earth?s gravity field studies 000193616 5203_ $$aThe motivation comes from the role of boundary value problems in Earth?s gravity field studies. The focus is on Neumann?s problem in the exterior of an oblate ellipsoid of revolution. The approach follows the concept of variational methods and the notionof the weak solution. The solution of the problem is approximated by linear combinations of basis functions with scalar coefficients, i.e. by Galerkin approximations. The aim is to discuss the construction of Galerkin?s matrix for elementary potentialsused in quality of a function basis. The computation of the entries of Galerkin?s matrix is expected to be simple for the elementary functions like these. Nevertheless, the opposite is true. Ellipsoidal harmonics are applied as a natural tool. The problem, however, is the summation of the series that represent the entries. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. 000193616 655_4 $$aaudiovizuální tvorba 000193616 7001_ $$aNesvadba, Otakar 000193616 7730_ $$92015$$dVienna:European Geosciences Union,2015. 000193616 85642 $$ahttps://www.rvvi.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F15%3A%230002195%21RIV16-GA0-00025615 000193616 910__ $$aABC039 000193616 980__ $$aclanky_vugtk 000193616 985__ $$aholota 000193616 985__ $$ariv 000193616 985__ $$autvar24 000193616 985__ $$anesvadba