eng
Holota, Petr
Nesvadba, Otakar
Boundary Complexity and Kernel Functions in Classical and Variational Concepts of Solving Geodetic Boundary Value Problems
https://www.rvvi.cz/riv?s=jednoduche-vyhledavani&ss=detail&h=RIV%2F00025615%3A_____%2F17%3AN0000038%21RIV18-GA0-00025615
In 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.
2018-07-13T07:27:44Z
http://knihovna.vugtk.cz/record/193407