J Austral Math Soc Ser B 34 pp419--438, 1993.

Remarks on the boundary element method for strongly nonlinear problems

Keijo Ruotsalainen

(Received 29 May 1990; revised 23 October 1991)

Abstract

Recently in several papers the boundary element method has been applied to nonlinear 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 L^p-spaces. Optimal order error estimates in L^p 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.

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Author

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

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Last Modified: Tue Aug 8 12:54:18 2000