arXiv subjects

Itatí Zocola

Publications and source records attributed to Itatí Zocola.

2 recordsLinked to original sources

arXiv2026

Error estimates for the patch bubble method for convection-dominated channel flow problem

We present error estimates for the BMZ (Bubble Mesh Zoom) residual-free bubble method applied to a convection-diffusion equation in the convection-dominated regime. The method incorporates both element bubbles and residual-free bubbles supported on patches of two adjacent elements. We focus on the case of a parallel flow in a square domain and derive error estimates in an energy norm that remain valid as diffusion becomes small. The theoretical findings are corroborated by numerical experiments, which also exhibit a competitive performance of the method.

math.NA↗

arXiv2025

Patch bubbles for advection-dominated steady and unsteady problems

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 Süli in 2005, but differs in the definition of the additional bubbles.

math.NA↗