000193618 001__ 193618 000193618 003__ CZ-ZdVUG 000193618 005__ 20190109112422.0 000193618 041__ $$aeng 000193618 040__ $$aABC039$$bcze 000193618 1001_ $$aHolota, Petr 000193618 24510 $$aOn the construction of Galerkin?s matrix for elementary potentials in case of an ellipsoidal solution domain in Earth?s gravity field studies 000193618 300__ $$a1 strana 000193618 5203_ $$aThe motivation comes from the role of boundary value problems in Earth?s gravity field studies. The focus is on Neumann?s problem in the exterior of an oblate ellipsoid of revolution. The approach follows the concept of variational methods and the notionof the weak solution. The solution of the problem is approximated by linear combinations of basis functions with scalar coefficients, i.e. by Galerkin approximations. The aim is to discuss the construction of Galerkin?s matrix for elementary potentialsused in quality of a function basis. The computation of the entries of Galerkin?s matrix is expected to be simple for the elementary functions like these. Nevertheless, the opposite is true. Ellipsoidal harmonics are applied as a natural tool. The problem, however, is the summation of the series that represent the entries. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. 000193618 655_4 $$asbornikove prispevky 000193618 7001_ $$aNesvadba, Otakar 000193618 7730_ $$92015$$dBratislava:Slovak University of Technology,2015.$$tXI Slovak Geophysical Conference$$z978-80-227-4447-8 000193618 85642 $$ahttps://www.rvvi.cz/riv?s=rozsirene-vyhledavani&ss=detail&n=0&h=RIV%2F00025615%3A_____%2F15%3A%230002190%21RIV16-GA0-00025615 000193618 910__ $$aABC039 000193618 980__ $$aclanky_vugtk 000193618 985__ $$aholota 000193618 985__ $$ariv 000193618 985__ $$autvar24 000193618 985__ $$anesvadba