Integration of a Priori Gravity Field Models in Boundary Element Formulations to Geodetic Boundary Value Problems

2001 ◽  
pp. 103-109
Author(s):  
Roland Klees ◽  
Rüdiger Lehmann
Keyword(s):  
Boundary Value Problems ◽  
Boundary Element ◽  
Gravity Field ◽  
Boundary Value ◽  
A Priori ◽  
Geodetic Boundary ◽  
Gravity Field Models

Laplacian structure, solution domain geometry and successive approximations in gravity field studies

2020 ◽  
Author(s):  
Petr Holota ◽  
Otakar Nesvadba
Keyword(s):  
Boundary Value Problems ◽  
Gravity Field ◽  
Laplace Operator ◽  
Boundary Value ◽  
Field Studies ◽  
Successive Approximations ◽  
Physical Surface ◽  
The Earth ◽  
Geodetic Boundary ◽  
The Laplace Operator

<p>When treating geodetic boundary value problems in gravity field studies, the geometry of the physical surface of the Earth may be seen in relation to the structure of the Laplace operator. Similarly as in other branches of engineering and mathematical physics a transformation of coordinates is used that offers a possibility to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. The Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a sphere or an oblate ellipsoid of revolution, even if these are optimally fitted. The situation may be more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. The structure of the Laplace operator, however, is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of geodetic boundary value problems expressed in terms of new coordinates. The structure of iteration steps is analyzed and if useful, it is modified by means of the integration by parts. Subsequently, the individual iteration steps are discussed and interpreted.</p>

scholarly journals Boundary value problems with nonlocal conditions for hyperbolic systems of equations with two independent variables

2020 ◽  
Vol 53 (2) ◽  
pp. 159-180
Author(s):  
V. M. Kyrylych ◽  
O. Z. Slyusarchuk
Keyword(s):  
Boundary Value Problems ◽  
A Priori Estimates ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Problems ◽  
Priori Estimates ◽  
Smooth Coefficients

Nonlocal boundary value problems for arbitrary order hyperbolic systems with one spatial variable are considered. A priori estimates for general nonlocal mixed problems for systems with smooth and piecewise smooth coefficients are obtained. The correct solvability of such problems is proved.Examples of additional conditions necessity are provided.

Explicit A Priori Inequalities with Applications to Boundary Value Problems.

1978 ◽  
Vol 32 (142) ◽  
pp. 656 ◽  
Author(s):  
L. P. ◽  
V. G. Sigillito
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
A Priori
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