Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems
Numerical Analysis
2025-07-14 v1 Numerical Analysis
Abstract
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an -matrix) on Voronoi polygonal meshes, provided their duals are Delaunay triangulations with acute angles. Furthermore, the study outlines a comprehensive framework for EAVE methodologies, introducing another variant that integrates with the stiffness matrix derived from the lowest-order virtual element method for the Poisson equation. Numerical experiments confirm the theoretical advantages of the monotonicity property and demonstrate an optimal convergence rate across various mesh configurations.
Cite
@article{arxiv.2402.13347,
title = {Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems},
author = {Shuhao Cao and Long Chen and Seulip Lee},
journal= {arXiv preprint arXiv:2402.13347},
year = {2025}
}