A nonlinear boundary value problem solved by spectral methods. (English) Zbl 0719.35025

We study a nonlinear boundary value problem posed on the interior or the exterior of the unit disk in \({\mathbb{R}}^ 2\). Using capacity operator, we transform it into a pseudo-differential problem posed on the unit circle. The Galerkin method, with Fourier developments, is used to approximate our problem. We show the convergence of the fixed-point scheme and we give an accurate bound of the \(L^ 2\)-norm of the error. Numerical results coming from a problem arising in electromagnetic casting are also presented.
Reviewer: Olivier Coulaud


35J65 Nonlinear boundary value problems for linear elliptic equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35S15 Boundary value problems for PDEs with pseudodifferential operators
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