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A high order numerical method for analysis and simulation of 2D semilinear Sobolev model on polygonal meshes

Author

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  • Singh, Ajeet
  • Cheng, Hanz Martin
  • Kumar, Naresh
  • Jiwari, Ram

Abstract

In this article, we design and analyze a hybrid high-order method for a semilinear Sobolev model on polygonal meshes. The method offers distinct advantages over traditional approaches, demonstrating its capability to achieve higher-order accuracy while reducing the number of unknown coefficients. We derive error estimates for the semi-discrete formulation of the method. Subsequently, these convergence rates are employed in full discretization with the Crank–Nicolson scheme. The method is demonstrated to converge optimally with orders of O(τ2+hk+1) in the energy-type norm and O(τ2+hk+2) in the L2 norm. The reported method is supported by a series of computational tests encompassing linear, semilinear and Allen–Cahn models.

Suggested Citation

  • Singh, Ajeet & Cheng, Hanz Martin & Kumar, Naresh & Jiwari, Ram, 2025. "A high order numerical method for analysis and simulation of 2D semilinear Sobolev model on polygonal meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 227(C), pages 241-262.
    • Handle: RePEc:eee:matcom:v:227:y:2025:i:c:p:241-262
    DOI: 10.1016/j.matcom.2024.08.010
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    References listed on IDEAS

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    1. Chen, Hao & Nikan, Omid & Qiu, Wenlin & Avazzadeh, Zakieh, 2023. "Two-grid finite difference method for 1D fourth-order Sobolev-type equation with Burgers’ type nonlinearity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 248-266.
    2. Poochinapan, Kanyuta & Wongsaijai, Ben, 2022. "Numerical analysis for solving Allen-Cahn equation in 1D and 2D based on higher-order compact structure-preserving difference scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).
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