Publication Cover
Applicable Analysis
An International Journal
Volume 46, 1992 - Issue 3-4
13
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On the galerkln boundary element method for a mixed non-linear boundary value problem

Pages 195-213 | Received 06 Sep 1989, Published online: 10 May 2007

References

  • K. Atkinson, G, Chandler, BIE methods for solving Laplace's equation with nonlinear boundary conditions: the smooth boundary case, to appear
  • Babuŝka , I. and Aziz , A.K. 1972 . “ Survey lectures on the mathematical foundations of the finite element method ” . In The Mathematical Foundation of the Finite Element Method with Applications to Partial Differential Equations , Edited by: Aziz , A.K. 3 – 359 . New York : Academic Press .
  • Barbu , V. 1978 . Nonlinear semigroups and differential equations in Banach spaces , Leyden : Noordhoff International Publishing .
  • Bialecki , R. and Novak , A.J. 1981 . Boundary value problems in heat conduction with nonlinear material and nonlinear boundary conditions . Appl. Math. Mod , 5 : 417 – 421 .
  • Brézis , H. 1972 . Problemes Unilatereaux . J. Math. Pures et Appl , 51 : 1 – 168 .
  • M. Costabel, Starke Elliptizität von Randintegraloperatoren erster Art,'.THD-Preprint Nr. 868 (Habilitationsschrift), Darmstadt (1984).
  • Costabel , M. and Stephan , E. 1985 . “ Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation ” . In Mathematical models and methods in mechanics , Banach Center Publication, Warsaw .
  • Hörmander , L. 1963 . Linear Partial Differential Operators , Berlin - Heidelberg - New York : Springer-Verlag .
  • Ingham , D.B. , Heggs , P.J. and Manzoor , M. 1981 . Boundary integral equation solution of non-linear plane potential problems . IMA. J. Numer. Anal , 1 : 415 – 426 .
  • Jörgens , K. 1970 . Lineare Integraloperatoren , Stuttgart : Teubner .
  • B. Kawohl, Uber nichtlineare gemischte Randwertprobleme für elliptische Differentialgleichungen zweiter Ordnung auf Gebieten mit Ecken', Thesis, Technische Hochschule Darmstadt, W.-Germany (1978).
  • Lions , J.L. and Magenes , E. 1972 . Non-homogeneous boundary value problems and applications , Vol. 1 , Heidelberg, , New York : Springer- Verlag, Berlin .
  • Oden , J.T. 1986 . Qualitative methods in nonlinear mechanics , New Jersey : Prentice-Hall Englewood Cliffs .
  • Pascali , D. and Sburlan , S. 1978 . Nonlinear Mappings of Monotone Type , Bucarest : Siijthioff and Noordhoff International Publishers .
  • Petryshyn , W.V. 1975 . On the approximation-solvability of equations involving a-proper and pseudo-a-proper mappings . Bull. of AMS. , 81 ( 2 ) : 223 – 312 .
  • Ruotsalainen , K. and Saranen , J. 1989 . On the collocation method for a non-linear boundary integral equation . J. Comp. and Appl. Math , 29 ( 2 ) : 339 – 348 .
  • Ruotsalainen , K. and Wendland , W.L. 1988 . On the boundary element method for some non-linear boundary value problems . Numer. Math , 53 ( 2 ) : 299 – 314 .
  • J. Saranen, Projection methods for a class of Hammerstein equations,SIAM J. Numer. Anal., to appear.
  • Saranen , J. and Wendland , W.L. 1985 . On the asymptotic convergence of collocation methods with spline functions of even degree . Math. Comp , 45 ( 2 ) : 91 – 108 .
  • Schumaker , L. 1975 . Spline Functions: Basic Theory , New York, , London : John Wiley and Sons .
  • Wendland , W.L. , Stephan , E. and Hsiao , G.C. 1979 . On the integral equation method for the plane mixed boundary value problem of the Laplacian . Math.Meth. in Appl.Sci , 1 : 265 – 321 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.