Extension to nonlinear problems

Abstract

The RB method is extended to the case of parametrized nonlinear PDEs. Examples are discussed concerning the Navier-Stokes equations and an elliptic semilinear equation. Both high-fidelity and RB approximations, as well as their interplay with Newton linearization, are analyzed, before considering in detail the case of Navier-Stokes equations. The underlying RB construction is essentially the same as for the previous linear PDEs, hence the focus is put on the characteristic aspects of the efficient treatment of nonlinear terms.