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A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation

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Abstract

We present a local projection stabilization for the virtual element discretization of the nonlinear convection–diffusion–reaction equation. We consider a streamline-derivative-based term for stabilization in the discrete formulation that preserves the stability property. We prove the optimal convergence estimates in the \(H^1\)- and \(L^2\)-norms. Numerical experiments consisting of different types of interior and boundary layers are conducted. The proposed numerical method captures the solution very well away from the layers. The numerical results show the proposed method’s better performance in comparison with the gradient-based local projection stabilization method.

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  1. Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, 695547, India

    Sudheer Mishra & E. Natarajan

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  1. Sudheer Mishra
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Mishra, S., Natarajan, E. A streamline-derivative-based local projection stabilization virtual element method for nonlinear convection–diffusion–reaction equation. Calcolo 60, 46 (2023). https://doi.org/10.1007/s10092-023-00539-z

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