Computing and Information SUPERCONVERGENT TECHNIQUES IN MULTI-SCALE METHODS

Abstract. It is well known that many problems of practical importance in science and engineering have multiple-scale solutions. Moreover, the calculations of numerical methods for these problems is very intensive, even if using some multi-scale proceedures. It is therefore important to seek efficient calculation methods. In this paper, superconvergent techniques are used in existing multiscale methods to improve the calculation efficiency. Furthermore, based on comprehensive analysis, the order of the error estimates between the numerical approximation and the exact solution is verified to be improved. Key Words. Elliptic equations, superconvergent technique, periodic microstructure, multi-scale methods, asymptotic expansion, homogenization. 1