Publication

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

Alfio Quarteroni, Andrea Manzoni, Yvon Maday
2016
Report or working paper
Abstract

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.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.