Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes Article Swipe

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Zaffar Mehdi Dar , M. Arrutselvi , M. Chandru , Sundararajan Natarajan , Gianmarco Manzini ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.3934/mine.2025005

We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the $ L^2 $-norm and $ H^1 $-norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.

Related Topics

Polygon Mesh

Convection

Mathematical Analysis

Performance Indicator

Operations Management

Law

Concepts

Polygon mesh Nonlinear system Convection–diffusion equation Element (criminal law) Diffusion Convection Diffusion equation Mathematical analysis Mathematics Applied mathematics Mechanics Physics Geometry Engineering Thermodynamics Quantum mechanics Political science Metric (unit) Operations management Law

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Type: article
Language: en
Landing Page: https://doi.org/10.3934/mine.2025005
OA Status: diamond
Cited By: 4
References: 56
Related Works: 10
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DOI: https://doi.org/10.3934/mine.2025005

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Title: Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes

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Language: en

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Publication year: 2025

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Publication date: 2025-01-01

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Authors: Zaffar Mehdi Dar, M. Arrutselvi, M. Chandru, Sundararajan Natarajan, Gianmarco Manzini

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Landing page: https://doi.org/10.3934/mine.2025005

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Concepts: Polygon mesh, Nonlinear system, Convection–diffusion equation, Element (criminal law), Diffusion, Convection, Diffusion equation, Mathematical analysis, Mathematics, Applied mathematics, Mechanics, Physics, Geometry, Engineering, Thermodynamics, Quantum mechanics, Political science, Metric (unit), Operations management, Law

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Cited by: 4

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