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Remarks on the boundary element method for strongly nonlinear problems

Published online by Cambridge University Press:  17 February 2009

Keijo Ruotsalainen
Keijo Ruotsalainen
Affiliation:
University of Oulu, Faculty of Technology, Section of Mathematics, SF-90570 Oulu, Finland.
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Abstract

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Recently in several papers the boundary element method has been applied to non-linear problems. In this paper we extend the analysis to strongly nonlinear boundary value problems. We shall prove the convergence and the stability of the Galerkin method in Lp spaces. Optimal order error estimates in Lp space then follow. We use the theory of A-proper mappings and monotone operators to prove convergence of the method. We note that the analysis includes the u4 -nonlinearity, which is encountered in heat radiation problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 4 , April 1993 , pp. 419 - 438
Copyright
Copyright © Australian Mathematical Society 1993

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