Skip to main content
SpringerLink
Log in

A solution to boundary value problems with over-specified boundary conditions

  • Brief Reports
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Summary

The problem of determining the unknown terms of a differential equation from over-specified boundary conditions is solved by means of the potential theory. The boundary values of compatibility functions adapting the differential equations to the prescribed boundary conditions are introduced as explicit unknowns in the system of linear equations. Two applications to fluid mechanics are presented, which demonstrate the efficiency of the method.

Résumé

Le problème de déterminer les termes inconnus d'une équation différentielle, à partir de conditions aux limites surdéterminées, est résolu au moyen de la théorie des potentiels. Les valeurs aux limites de fonctions de compatibilité adaptant les équations différentielles aux conditions aux limites prescrites sont introduites, comme inconnues explicites, dans le système des équations intégrales linéaires. Deux applications à la mécanique des fluides sont présentées, qui démontrent l'efficacité de la méthode.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. R. Cannon,A class of inverse problems: the determination of second order elliptic partial differential operators from over-specified boundary data, in Improperly posed boundary value problems, Pitman, London 1975.

    Google Scholar 

  2. P. M. Morse and H. Feshbach,Methods of theoretical physics. McGraw-Hill, New-York 1953.

    Google Scholar 

  3. M. Ribaut and R. Scheld,A hybrid method for calculating vector fields subject to inhomogeneous boundary conditions. Z. angew. Math. Phys.30, 503–513 (1979).

    Google Scholar 

  4. H. Niessner and M. Ribaut,Conditions of boundary integral equations arising from flow computations, to be published in J. Comput. & Appl. Math. Proc. of the ICCAM, Leuven 1984.

  5. F. D. Gakhov,Boundary value problems. Pergamon Press, Oxford 1966.

    Google Scholar 

  6. M. Ribaut,On the calculation of three-dimensional divergent and rotational flow in turbomachines. JFE99, 187–196 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AG Brown, Boveri & Cie, Baden

    M. Ribaut

Authors
  1. M. Ribaut
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ribaut, M. A solution to boundary value problems with over-specified boundary conditions. Z. angew. Math. Phys. 36, 629–634 (1985). https://doi.org/10.1007/BF00945303

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00945303

Keywords

Search

Navigation