Error estimates for the patch bubble method for convection-dominated channel flow problem
This work addresses error analysis for a specific numerical method in fluid dynamics, providing incremental theoretical validation for convection-dominated problems.
The paper tackled error estimation for the BMZ residual-free bubble method applied to convection-dominated channel flow, deriving energy norm estimates that remain valid as diffusion decreases and showing competitive performance in numerical experiments.
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.