AuthorsA. E. Løvgren, E. M. Rønquist, and Y. Maday
EditorsC. Calgaro, J. Coulombel, and T. Goudon
TitleThe Reduced Basis Element Method for Fluid Flows
Afilliation, Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
Publication TypeBook Chapter
Year of Publication2007
Book TitleAnalysis and Simulation of Fluid Dynamics
Secondary TitleAdvances in Mathematical Fluid Mechanics
Place PublishedBasel
ISBN Number978-3-7643-7741-0

The reduced basis element approximation is a discretization method for solving partial differential equations that has inherited features from the domain decomposition method and the reduced basis approximation paradigm in a similar way as the spectral element method has inherited features from domain decomposition methods and spectral approximations. We present here a review of the method directed to the application of fluid flow simulations in hierarchical geometries. We present the rational and the basics of the method together with details on the implementation. We illustrate also the rapid convergence with numerical results.