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<p>In this paper, we introduce a discrete duality finite volume (DDFV) scheme for solving a coupled nonlinear parabolic-elliptic system. This system corresponds to the Keller-Segel model for chemotaxis, which describes the movement of living cells or organisms in response to chemical gradients. We begin by establishing bounds for the sequences of approximate solutions and prove their existence. Then, using compactness arguments tailored to parabolic problems, we demonstrate the convergence to a weak solution. Finally, numerical results are presented to highlight the efficiency of the approach and illustrate the behavior of cell density under chemical attraction.</p>

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Numerical analysis of a finite volume scheme for a parabolic-elliptic system with nonlinear diffusion and a convection term

  • 期刊论文

  • 发表日期：

    2025年2月23日

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  • Hicham El Moutaouakil,
  • Mohamed Rhoudaf

摘要

In this paper, we introduce a discrete duality finite volume (DDFV) scheme for solving a coupled nonlinear parabolic-elliptic system. This system corresponds to the Keller-Segel model for chemotaxis, which describes the movement of living cells or organisms in response to chemical gradients. We begin by establishing bounds for the sequences of approximate solutions and prove their existence. Then, using compactness arguments tailored to parabolic problems, we demonstrate the convergence to a weak solution. Finally, numerical results are presented to highlight the efficiency of the approach and illustrate the behavior of cell density under chemical attraction.