Construction of RB spaces by the greedy algorithm

Abstract

We describe another, indeed very popular, approach to construct a reduced basis space in the context of parametrized PDEs: the so-called greedy algorithm. This consists in an iterative sampling from the parameter space fulfilling at each step a suitable optimality criterion that relies on the a posteriori error estimate. We illustrate the main features of this procedure in the algebraic RB framework, and then address its continuous counterpart, discuss some a priori convergence results and verify them using numerical tests.