A nonlinear boundary value problem solved by spectral methods

Olivier Coulaud (1) , Antoine Henrot (1)

1 NUMATH - Mathematical Analysis and Numerical Simulation of Non-Linear Models

We study a nonlinear boundary value problem posed in the interior or the exterior of the unit disk in R2. Using capacity operator, we transform it into a pseudo-differential problem on the unit circle. The Galerkin method together with Fourier expansion, is used to approximate our problem. We show the convergence of the fixed-point scheme and we give an accurate bound of the L2-norm of the error. Numerical results coming from a problem arising in electromagnetic casting are also presented.

Mots clés: nonlinear boundary value problem; fixed-point; Galerkin; spectral methods

Domaines: Autre [cs.OH]

Olivier Coulaud, Antoine Henrot. A nonlinear boundary value problem solved by spectral methods. [Research Report] RR-1252, INRIA. 1990, pp.18. ⟨inria-00075306⟩