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

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

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 227, issue C, 241-262

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.

Keywords: Semilinear Sobolev model; Hybrid high-order methods; Semidiscrete and fully discrete schemes; Error estimates; Polygonal meshes (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:227:y:2025:i:c:p:241-262

DOI: 10.1016/j.matcom.2024.08.010

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