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The nullfield method for the ellipsoidal Stokes problem

Authors
  • Ritter, S.1
  • 1 Mathematisches Institut II, Universität Karlsruhe, D-76128 Karlsruhe, Germany Phone: +49 721 608 2048; Fax: +49 721 608 2051; email: [email protected], DE
Type
Published Article
Journal
Journal of Geodesy
Publisher
Springer-Verlag
Publication Date
Feb 01, 1998
Volume
72
Issue
2
Pages
101–106
Identifiers
DOI: 10.1007/s001900050151
Source
Springer Nature
Keywords
License
Yellow

Abstract

The ellipsoidal Stokes problem is one of the basic boundary-value problems for the Laplace equation which arises in physical geodesy. Up to now, geodecists have treated this and related problems with high-order series expansions of spherical and spheroidal (ellipsoidal) harmonics. In view of increasing computational power and modern numerical techniques, boundary element methods have become more and more popular in the last decade. This article demonstrates and investigates the nullfield method for a class of Robin boundary-value problems. The ellipsoidal Stokes problem belongs to this class. An integral equation formulation is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. Explicit expressions for the eigenvalues and eigenfunctions for the boundary integral operator are provided.

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