Two-Scale Curved Element Method for Elliptic Problems with Small Periodic Coefficients

Abstract

This paper is concerned with the second order elliptic problems with small periodic coefficients on a bounded domain with a curved boundary. A two-scale curved element method which couples linear elements and isoparametric elements is proposed. The error estimate is obtained over the given smooth domain. Furthermore, an additive Schwarz method is provided for the isoparametric element method.