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. Altough this approach was considered for the Helmholtz equation before, our new insights show that some of its important properties have remained hidden.
After revision:  A new two-level finite element method is introduced for the approximations of the bubble functions.