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On the boundary element method for some nonlinear boundary value problems

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Summary

Here we analyse the boundary element Galerkin method for two-dimensional nonlinear boundary value problems governed by the Laplacian in an interior (or exterior) domain and by highly nonlinear boundary conditions. The underlying boundary integral operator here can be decomposed into the sum of a monotoneous Hammerstein operator and a compact mapping. We show stability and convergence by using Leray-Schauder fixed-point arguments due to Petryshyn and Nečas.

Using properties of the linearised equations, we can also prove quasioptimal convergence of the spline Galerkin approximations.

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Authors and Affiliations

  1. Section of Mathematics, University of Oulu, Faculty of Technology, SF-90570, Oulu, Finland

    K. Ruotsalainen

  2. Mathematisches Institut A, University of Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Germany

    W. Wendland

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  1. K. Ruotsalainen
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  2. W. Wendland
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This work was carried out while the first author was visiting the University of Stuttgart

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Ruotsalainen, K., Wendland, W. On the boundary element method for some nonlinear boundary value problems. Numer. Math. 53, 299–314 (1988). https://doi.org/10.1007/BF01404466

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