Chapter 2: Reduced Basis Methods for Parametrized PDEs—A Tutorial Introduction for Stationary and Instationary Problems

2.1 ▪ Abstract In this part we are concerned with a class of model reduction techniques for parametric partial differential equations (PDEs), the so-called reduced basis (RB) methods. These allow us to obtain low-dimensional parametric models for various complex applications, enabling accurate and rapid numerical simulations. Important aspects are basis generation and certification of the simulation results by suitable a posteriori error control. The main terminology, ideas, and assumptions will be explained for the case of linear stationary elliptic, as well as parabolic or hyperbolic, instationary problems. Reproducible experiments will illustrate the theoretical findings. We close with a discussion of further recent developments.