Numerical zoom for multiscale problems with an application to nuclear waste disposal

We analyse here a computational technique and error estimates for the numerical solution of some problems with multiple scales when the small scale is confined to geometrically small regions such as jumps of coefficients on curves and surfaces or complex variations of coefficients in small regions where numerical zooms can be made. The method is an adaptation of the Hilbert Subspace Decomposition Method studied by the second author in a different context so the method is restated with all known results. Combined with the layer decomposition of [S. Delpino, O. Pironneau, Asymptotic analysis and layer decomposition for the Couplex exercise, in: Alain Bourgeat, Michel Kern (Eds.), Computational Geosciences, vol. 8. No. 2, Kluwer Academics Publishers, 2004, pp. 149–162] the method is applied to the numerical assessment of a nuclear waste repository site.