Resumen de Spectral and finite elements for an exterior problem in the plane

Antonio Márquez Gentil, Salim Meddahi Bouras

• We present a Galerkin BEM–FEM scheme based on a combination of spectral and finite element methods to solve numerically an exterior Poisson problem in the plane. We provide error estimates for the Galerkin method, propose a fully discrete scheme based on elementary quadrature formulas and show that the perturbation due to this numerical integration still preserves the rate of convergence. The advantage of using a spectral approximation for the unknown defined on the boundary is that few degrees of freedom are needed on this interface. Therefore, the global system of linear equations associated to the fully discrete problem is easier to solve as we show in our numerical experiments.