Istituto di Matematica Applicata e Tecnologie Informatiche     
Sangalli G. Capturing small scales in elliptic problems using a Residual-Free Bubbles Finite Element Method. Preprint ercim.cnr.ian//2002-1292, 2002.
In this work we study the Residual-Free Bubbles (RFB) finite element method for solving second order elliptic equations with rapidly varying coefficients. The RFB technique is closely related to both the Multi-scale Finite Element Method (MsFEM) introduced by T. Hou and collaborators, and the upscaling procedures which are very common in the engineering literature for solving this kind of partial differential equation. We also introduce a variation of the RFB method, based on macro-bubbles and referred as Residual-Free Macro-Bubbles (RFMB) method, which gives more accurate numerical solutions. In the case of periodic coefficients we are able to prove the a priori error estimates for the methods. Eventually, we test the numerical methods on model problems.
Subject Multiscale
Finite element

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