Before revision:  A new two-level finite element method is introduced for the approximations of the residual-free bubble (RFB) functionsand its application to the Helmholtz equation with large wave numbers is considered.
After revision: An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the residual-free bubble (RFB) functionsand its application to the Helmholtz equation with large wave numbers is considered.