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Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes

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Abstract

In this paper, we analyze the virtual element method for the quasilinear convection-diffusion-reaction equation. The most important part in the analysis is the proof of existence and uniqueness of the branch of solution of the discrete problem. We extend the explicit analysis given by Lube (Numer. Math. 61, 335–357, 1992) for the finite element discretization to virtual element framework. We prove the optimal rate of convergence in the energy norm. In order to reduce the overall computational cost incurred for the nonlinear equations, we have performed the numerical experiments using a two-grid method. We validate the theoretical estimates with the computed numerical results.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    M. Arrutselvi & S. Natarajan

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

    E. Natarajan

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  1. M. Arrutselvi
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  2. E. Natarajan
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  3. S. Natarajan
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Communicated by: Ilaria Perugia

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Arrutselvi, M., Natarajan, E. & Natarajan, S. Virtual element method for the quasilinear convection-diffusion-reaction equation on polygonal meshes. Adv Comput Math 48, 78 (2022). https://doi.org/10.1007/s10444-022-09990-y

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