MATHICSE Technical Report : An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems

We propose a new, black-box online stabilization strategy for reduced basis (RB) approx- imations of parameter-dependent advection-diffusion problems in the advection-dominated case. Our goal is to stabilize the RB problem irrespectively of the stabilization (if any) op- erated on the high-fidelity (e.g. finite element) approximation, provided a set of stable RB functions have been computed. Inspired by the spectral vanishing viscosity method, our ap- proach relies on the transformation of the basis functions into of modal basis, then on the addition of a vanishing viscosity term over the high RB modes, and on a rectification stage { prompted by the spectral filtering technique { to further enhance the accuracy of the RB approximation. Numerical results dealing with an advection-dominated problem parametrized with respect to the diffusion coefficient show the accuracy of the RB solution on the whole parametric range.