SIGEST

Abstract

The SIGEST paper in this issue, “The Validity of Johnson--Nédélec's BEM--FEM Coupling on Polygonal Interfaces” by Francisco-Javier Sayas, is from the SIAM Journal on Numerical Analysis. The paper resolves a thirty-year old question about the coupling of the boundary element method (BEM) with the finite element method (FEM) for problems that need both. For example, a problem which naturally contains both an exterior (or infinite) domain and an interior (or bounded) domain might best be solved by discretizing the exterior and interior with FEM and the interface or boundary with BEM. The Johnson--Nédélec coupling was the earliest such method. While this coupling has been successful in practice, the assumptions for the underlying theory did not hold in many situations, including problems with nonsmooth boundaries and linear elasticity. Hence, the theory did not apply to the polygonal interfaces that arise in many finite element discretizations. This led to a perception by some that the Johnson--Nédélec coupling was not sufficient for such problems. In this paper the author shows that in some situations the Johnson--Nédélec coupling works for any Lipschitz boundary and any choice of discrete spaces, thereby putting an old question to rest.