Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition
Abstract. Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e20)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant.
Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition
Abstract. Green's function for the boundary-value problem of Stokes's type with ellipsoidal corrections in the boundary condition for anomalous gravity is constructed in a closed form. The `spherical-ellipsoidal' Stokes function describing the effect of two ellipsoidal correcting terms occurring in the boundary condition for anomalous gravity is expressed in O(e20)-approximation as a finite sum of elementary functions analytically representing the behaviour of the integration kernel at the singular point ψ=0. We show that the `spherical-ellipsoidal' Stokes function has only a logarithmic singularity in the vicinity of its singular point. The constructed Green function enables us to avoid applying an iterative approach to solve Stokes's boundary-value problem with ellipsoidal correction terms involved in the boundary condition for anomalous gravity. A new Green-function approach is more convenient from the numerical point of view since the solution of the boundary-value problem is determined in one step by computing a Stokes-type integral. The question of the convergence of an iterative scheme recommended so far to solve this boundary-value problem is thus irrelevant.
Construction of Green's function for the Stokes boundary-value problem with ellipsoidal corrections in the boundary condition
Martinec, Z. (Autor:in)
Journal of Geodesy ; 72
1998
Aufsatz (Zeitschrift)
Englisch
BKL:
38.73
Geodäsie
Stokes' Second Problem with Velocity Slip Boundary Condition
| British Library Online Contents | 2011
TECHNICAL PAPERS - Green's Function for Mixed Boundary Value Problem of Thin Plate
| Online Contents | 2000
Green's Function of Thermoelastic Mixed Boundary Value Problem for an Elliptic Hole
| Online Contents | 2001
Green's function solution to spherical gradiometric boundary-value problems
| Online Contents | 2003
Solutions of the linearized geodetic boundary value problem for an ellipsoidal boundary to order e3
| Online Contents | 2003