Composite mesh difference methods for elliptic boundary value problems

Summary The purpose of this paper is to develop composite mesh difference methods for elliptic boundary value problems over regions with curved, smooth boundaries. A curved mesh will cover an annular strip along the boundary of the region which is included in the mesh. For the rest of the region and for a suitable inner part of the annular strip a square or rectangular mesh will be used. On each mesh a difference approximation is set up as well as couplings between them. Only second order methods for second order elliptic equations will be treated in detail.This research was supported by the Swedish Institute for Applied Mathematics (ITM)