A nonlinear boundary value problem solved by spectral methods

Abstract

We study a nonlinear boundary value problem posed on the interior or the exterior of the unit disk in R². 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 L²-norm of the error. Numerical results coming from a problem arising in electromagnetic casting are also presented

Keywords:

• Nonlinear boundary value problem
• fixed point
• Galerkin
• spectral methods

AMS(MOS)::

• 35A40
• 35J65
• 65N35