Patch bubbles for advection-dominated steady and unsteady problems
Numerical Analysis
2025-12-30 v2 Numerical Analysis
Abstract
A novel variant of the \emph{residual-free bubble} method (RFB) for advection dominated problems is presented. Since the usual RFB still suffers from oscillations and strong under/overshoots, the bubble space is enriched by \emph{patch bubbles}, giving more freedom to the bubble space. We use a recursive and efficient approach to accurately compute the bubbles. Numerical experiments clearly demonstrate the superiority of our method compared to the standard RFB. The method is similar to the \emph{enhanced residual-free bubble} method (eRFB) proposed by Cangiani and S\"uli in 2005, but differs in the definition of the additional bubbles.
Cite
@article{arxiv.2504.21835,
title = {Patch bubbles for advection-dominated steady and unsteady problems},
author = {Eberhard Bänsch and Pedro Morin and Itatí Zocola},
journal= {arXiv preprint arXiv:2504.21835},
year = {2025}
}