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Mathematics of Computation

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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
Published electronically: June 12, 2000
MathSciNet review: 1826575
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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

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

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