A reduced-basis element method

Reduced basis methods are particularly attractive to use in order to diminish the number of degrees-of-freedom associated with the approximation to a set of partial differential equations. The main idea is to construct ad hoc basis functions with a large information content. In this Note, we propose to develop and analyze reduced basis methods for simulating hierarchical flow systems, which is of relevance for studying flows in a network of pipes, an example being a set of arteries or veins. We propose to decompose the geometry into generic parts (e.g., pipes and bifurcations), and to construct a reduced basis for these generic parts by considering representative geometric snapshots. The global system is constructed by gluing the individual basis solutions together via Lagrange multipliers. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.