000193407 001__ 193407
000193407 005__ 20181127114100.0
000193407 041__ $$aeng
000193407 1001_ $$aHolota, Petr
000193407 24510 $$aBoundary Complexity and Kernel Functions in Classical and Variational Concepts of Solving Geodetic Boundary Value Problems
000193407 300__ $$a10 stran
000193407 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.
000193407 655_4 $$aanotace
000193407 653_0 $$aGreen’s function
000193407 653_0 $$aGalerkin’s system
000193407 653_0 $$areproducing kernel
000193407 653_0 $$aelliptic integrals
000193407 653_0 $$aLaplace’s operator
000193407 653_0 $$atransformation of coordinates
000193407 7001_ $$aNesvadba, Otakar
000193407 7730_ $$92017$$dCham, Springer, 2017$$tProceedings of the Joint Scientific Assembly of the International Association of Geodesy and the International Association of Seismology and Physics of the Earth’s Interior (IAG-IASPEI 2017)$$x0939-9585
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000193407 985__ $$aholota