An Optimal Iterative Process for the Johnson--Nedelec Method of Coupling Boundary and Finite Elements

Abstract

We reformulate the discretization of the Johnson--Nedelec method [11] of coupling boundary elements and finite elements for an exterior bidimensional Laplacian. This new formulation leads to optimal error estimates and allows the use of simple quadrature formulas for calculation of the boundary element matrix. We show that if the parameter of discretization is sufficiently small, the fully discrete scheme is well posed and the error estimates remain unaltered. The rest of the paper is devoted to the study of an efficient algorithm for solving the resulting discrete linear systems.