000193408 001__ 193408
000193408 005__ 20210518130520.0
000193408 041__ $$aeng
000193408 1001_ $$aHolota, Petr
000193408 24510 $$aBoundary Complexity in Classical and Variational Concepts of Solving Geodetic Boundary Value Problems
000193408 5203_ $$9eng$$aIn gravity field studies the complex structure of the Earth’s surface makes the solution of geodetic boundary value problems quite challenging. This equally concerns classical methods of potential theory as well as modern methods often based on a (variational or) weak solution concept. Aspects of this nature are reflected in the content of the paper. In case of a spherical Neumann problem the focus is on the classical Green’s function method and on the use of reproducing kernel and elementary potentials in generating function bases for Galerkin’s approximations. Similarly, the use of reproducing kernel and elementary potentials is also highlighted for Galerkin’s approximations to the solution of Neumann’s problem in the exterior of an oblate ellipsoid of revolution. In this connection the role of elliptic integrals is pointed out. Finally, two concepts applied to the solution of the linear gravimetric boundary value problem are mentioned. They represent an approach based on variational methods and on the use of a transformation of coordinates offering an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. Successive approximations are involved in both the cases.
000193408 655_4 $$aanotace
000193408 653_0 $$aGreen’s function
000193408 653_0 $$aGalerkin’s system
000193408 653_0 $$areproducing kernel
000193408 653_0 $$aelliptic integrals
000193408 653_0 $$aLaplace’s operator
000193408 653_0 $$atransformation of coordinates
000193408 7001_ $$aNesvadba, Otakar
000193408 7730_ $$92017
000193408 85642 $$uhttps://www.rvvi.cz/riv?s=jednoduche-vyhledavani&ss=detail&h=RIV%2F00025615%3A_____%2F17%3AN0000043%21RIV18-GA0-00025615
000193408 85640 $$uhttp://www.iag-iaspei-2017.jp/programbook.html
000193408 943__ $$aRIV:O
000193408 980__ $$aclanky_vugtk
000193408 985__ $$aanotace
000193408 985__ $$ariv
000193408 985__ $$aholota