Submitted

Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems

Shuhao Cao, Long Chen and Seulip Lee

Submitted

Coming soon   Bibtex coming soon

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 $M$-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.