Local change of coordinates for grid-functions on regions with curved boundary

Abstract

Local change of coordinates, providing an appropriate transformation of functions on a domain Ω ∩ Rn into functions on Rn and R+n, is a well-known and frequently used technical tool in the theory of Sobolev-spaces Wm,p (Ω) and partial differential equations. In this paper we propose a corresponding transformation mapping grid-functions on regular grids Ωh into functions on Rnh and Rnh,+ which as in the continuous case can be used to remedy various difficulties arising the curved boundary of Ω.