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<p>The primary goal of this article is to propose an efficient virtual element method formulation for solving a two-dimensional time-fractional Emden-Fowler model. The virtual element technique is a generalization of the finite element approach to polygonal and polyhedral meshes in the Galerkin approximation framework. A fully discrete virtual element scheme is obtained by using a fractional version of the Grünwald-Letnikov approximation for the temporal discretization and the virtual element method for the spatial discretization. We establish the existence and uniqueness of the discrete solution, that is, the well-posedness of the approach. The error analysis and optimal convergence order with respect to the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>norm and the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^1-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>1</mn> </msup> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>seminorm are presented. The numerical experiments validated the theoretical analysis and demonstrated the technique’s efficacy on convex and non-convex polygonal meshes.</p>

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A conforming virtual element method for Emden-Fowler model over polygonal meshes

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Zaffar Mehdi Dar,
  • M. Arrutselvi,
  • Chandru Muthusamy,
  • Sundararajan Natarajan

摘要

The primary goal of this article is to propose an efficient virtual element method formulation for solving a two-dimensional time-fractional Emden-Fowler model. The virtual element technique is a generalization of the finite element approach to polygonal and polyhedral meshes in the Galerkin approximation framework. A fully discrete virtual element scheme is obtained by using a fractional version of the Grünwald-Letnikov approximation for the temporal discretization and the virtual element method for the spatial discretization. We establish the existence and uniqueness of the discrete solution, that is, the well-posedness of the approach. The error analysis and optimal convergence order with respect to the \(L^2-\) L 2 - norm and the \(H^1-\) H 1 - seminorm are presented. The numerical experiments validated the theoretical analysis and demonstrated the technique’s efficacy on convex and non-convex polygonal meshes.