Conforming spectral domain decomposition schemes

Abstract

Spectral domain decomposition schemes are presented for the numerical solution of second and fourth order problems. These schemes, which are formulated in the collocation framework yield spectral approximations which are conforming along the subdomain interfaces for both conforming and non-conforming decompositions. For conforming decompositions the approximations are pointwise C1 continuous across the interfaces for second order problems and C3 continuous across the interfaces for fourth order problems. For non-conforming decompositions the corresponding approximations are pointwise C0 and C1 continuous for second and fourth order problems, respectively. Efficient direct methods for the solution of the resulting systems are also presented. © Springer-Verlag Berlin Heidelberg 1997.