A MULTISCALE FINITE ELEMENT METHOD

We propose a multiscale nite element method to treat singularly perturbed reaction diusion equations. We enrich the usual piecewise linear or bilinear nite el- ement trial spaces with local solutions of the original problem, as in the Residual Free Bubble (RFB) setting, but do not require these functions to vanish on each element edge. Such multiscale functions have an analytic expression as long as the data are assumed to be linear. We enrich the space of test functions with bubbles allowing for static condensa- tion, thus our method is of Petrov-Galerkin type. We perform error analysis in dier ent asymptotic regimes and present numerical validations.