Reduced Basis Method for Parametrized Advection-Reaction Problems
Thursday 6th September 2007
In this work we consider the Reduced Basis method for the solution of parametrized advection-reaction partial differential equations. For generation of the basis we adopt a stabilized Finite Element method and we define the Reduced Basis method in the primal-dual formulation for this stabilized problem. We provide both a priori and a posteriori Reduced Basis error estimates and we discuss the effects of the Finite Element approximation on the Reduced Basis error. We propose an adaptive algorithm for the selection of the sample sets upon which thew basis are built. The basis idea of this algorithm is the minimization of the computational costs associated with the solution of the Reduced Basis problem. Numerical tests shows the convenience, in terms of computational costs, of the prime-dual Reduced Basis approach.