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Virtual Element Method for Nonlinear Time-Dependent Convection-Diffusion-Reaction Equation

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In this paper, we study the numerical solution of nonlinear time dependent convection-diffusion-reaction equation using virtual element method. We have used Virtual element discretization over polygonal meshes along with Streamline upwind Petrov–Galerkin stabilization (VEM-SUPG). The discrete terms are suitably modified to ensure the VEM computability with the help of projection operators \( {\Pi}_p^0 \) and \( {\Pi}_p^{\nabla } \) respectively. For the time discretization, we used backward Euler finite difference method and the resulting nonlinear system is solved using Newton’s method. We have conducted several numerical experiments validating the performance of VEM-SUPG method along with rate of convergence and behavior of solutions over convex and non-convex polygonal meshes.

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Authors and Affiliations

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

    M. Arrutselvi & E. Natarajan

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  1. M. Arrutselvi
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  2. E. Natarajan
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Correspondence to M. Arrutselvi.

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Arrutselvi, M., Natarajan, E. Virtual Element Method for Nonlinear Time-Dependent Convection-Diffusion-Reaction Equation. Comput Math Model 32, 376–386 (2021). https://doi.org/10.1007/s10598-021-09537-8

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