Boundary element methods for potential problems with nonlinear boundary conditions

Authors:
M. Ganesh and O. Steinbach

Journal:
Math. Comp. **70** (2001), 1031-1042

MSC (2000):
Primary 31C20, 65L20, 65N38, 74S15

DOI:
https://doi.org/10.1090/S0025-5718-00-01266-7

Published electronically:
June 12, 2000

MathSciNet review:
1826575

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Galerkin boundary element methods for the solution of novel first kind Steklov-Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in two- and three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations, we propose practical variants of the Galerkin scheme and give corresponding error estimates. We also discuss the actual implementation process with suitable preconditioners and propose an optimal hybrid solution strategy.

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Additional Information

**M. Ganesh**

Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia

Email:
ganesh@maths.unsw.edu.au

**O. Steinbach**

Affiliation:
Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Email:
steinbach@mathematik.uni-stuttgart.de

DOI:
https://doi.org/10.1090/S0025-5718-00-01266-7

Keywords:
Boundary element methods,
Nonlinear boundary conditions

Received by editor(s):
September 10, 1998

Received by editor(s) in revised form:
November 3, 1998, and July 30, 1999

Published electronically:
June 12, 2000

Additional Notes:
Part of this work was carried out while the second author was a Visiting Fellow in the School of Mathematics, UNSW, under an Australian Research Council Grant. The support of the Australian Research Council is gratefully acknowledged by both authors.

Dedicated:
Dedicated to Professor Ian Sloan on the occasion of his 60th birthday

Article copyright:
© Copyright 2000
American Mathematical Society