Conforming spectral approximations for non-conforming domain decompositions

Abstract

A spectral domain decomposition scheme is introduced for the numerical solution of second- and fourth-order elliptic problems. The technique is applicable to certain domain decompositions of rectangular or rectangularly decomposable domains. It is shown that it yields approximations which are pointwise C 0 continuous across the subdomain interfaces for second order problems and pointwise C 1 continuous across the subdomain interfaces for fourth-order problems.