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Boundary element methods for potential problems with nonlinear boundary conditions. (English) Zbl 0971.65107

Authors’ summary: 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.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
65F35 Numerical computation of matrix norms, conditioning, scaling
35J65 Nonlinear boundary value problems for linear elliptic equations
65N15 Error bounds for boundary value problems involving PDEs
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