CIP-stabilized Virtual Elements for diffusion-convection-reaction problems

TL;DR

This paper introduces a CIP-stabilized Virtual Element Method for diffusion-convection-reaction problems, enhancing stability in convection-dominated regimes through a continuous interior penalty approach and providing theoretical and numerical validation.

Contribution

It develops a quasi-robust Virtual Element Method with CIP stabilization tailored for convection-dominated diffusion-reaction problems, addressing stability challenges due to polynomial projections.

Findings

The method achieves stability in convection-dominated regimes.

Numerical tests confirm the theoretical error estimates.

The approach effectively handles advective terms in VEM.

Abstract

The Virtual Element Method for diffusion-convection-reaction problems is considered. In order to design a quasi-robust scheme also in the convection-dominated regime, a Continuous Interior Penalty approach is employed. Due to the presence of polynomial projection operators, typical of the Virtual Element Method, the stability and the error analysis require particular care, especially in treating the advective term. Some numerical tests are presented to support the theoretical results.