Communications in Mathematical Sciences

Volume 9 (2011)

Number 4

Residual-free bubble methods for numerical homogenization of elliptic problems

Pages: 1163 – 1176



Tao Yu (Department of Mathematics, University of Science and Technology of China, Hefei)

Xingye Yue (Department of Mathematics, Soochow University, Suzhou, China)


The residual-free bubble (RFB) method was first proposed for convection-diffusion problems. Then it was used to treat elliptic homogenization problems. We revisit it in this paper and try to reveal its relations to some other multiscale methods. Some new bubble schemes are also proposed.


residual-free bubble, numerical homogenization, multiscale finite element method, heterogeneous multiscale method, adaptive sampling

2010 Mathematics Subject Classification


Published 29 July 2011