Published

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

Shuhao Cao, Long Chen and Seulip Lee

Journal of Scientific Computing (2025) 104:70

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ABSTRACT:

This paper 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.