A New Stabilized Virtual Element Method for the Convection-Diffusion Equation

Abstract

We present a novel stabilized virtual element approximation for the convection-diffusion equation on polygonal meshes in convection-dominated regimes. We introduce a local projection-based stabilization technique to address convection-dominated regimes. The proposed stabilization technique relies on the streamline flow. We establish the well-posedness of the discrete problem. Furthermore, we have shown optimal convergence estimates in the energy norm. Notably, our proposed stabilization method offers simplicity in implementation and circumvents the need for second-order derivative terms. Additionally, we have outlined the implementation details of our method. To validate our theoretical findings, we have conducted several numerical experiments. Numerical results show the robustness of the proposed method with respect to diffusion parameters, confirming optimal convergence rates.

Keywords

Virtual element / Local projection stabilization (LPS) / Convection-diffusion / General polygons / 65N12 / 65N30

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