Noncorming matching conditions for coupling spectral and finite element methods

Abstract The aim of the paper is to propose and to study some discretization procedures for a second-order elliptic problem, which couple a spectral method and a finite element method: the domain is divided in two parts, and each method is used on one part. Two different matching conditions on the interface are described, leading to two different discrete problems, and an iterative algorithm of resolution is given for each condition. We provide a numerical analysis to compare them.