01604nas a2200133   4500008004100000245010100041210006900142260001900211490000800230520099000238653009201228100002101320856012901341       2014                        eng d00aFundamentals of Reduced Basis Method for problems governed by parametrized PDEs and applications0 aFundamentals of Reduced Basis Method for problems governed by pa  aWienbSpringer0 v5543 a<p>In this chapter we consider Reduced Basis (RB) approximations of parametrized Partial Differential Equations (PDEs). The the idea behind RB is to decouple the generation and projection stages (Offline/Online computational procedures) of the approximation process in order to solve parametrized PDEs in a fast, inexpensive and reliable way. The RB method, especially applied to 3D problems, allows great computational savings with respect to the classical Galerkin Finite Element (FE) Method. The standard FE method is typically ill suited to (i) iterative contexts like optimization, sensitivity analysis and many-queries in general, and (ii) real time evaluation. We consider for simplicity coercive PDEs. We discuss all the steps to set up a RB approximation, either from an analytical and a numerical point of view. Then we present an application of the RB method to a steady thermal conductivity problem in heat transfer with emphasis on geometrical and physical parameters.</p>10areduced basis method, linear elasticity, heat transfer, error bounds, parametrized PDEs1 aRozza, Gianluigi  uhttps://www.math.sissa.it/publication/fundamentals-reduced-basis-method-problems-governed-parametrized-pdes-and-applications