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

IF 4.4 2区 数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Ajeet Singh , Hanz Martin Cheng , Naresh Kumar , Ram Jiwari
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引用次数: 0

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.

多边形网格上二维半线性索波列夫模型分析与模拟的高阶数值方法
本文设计并分析了多边形网格上半线性索波列模型的混合高阶方法。与传统方法相比,该方法具有明显优势,在减少未知系数数量的同时实现了更高阶的精度。我们得出了该方法半离散形式的误差估计值。随后,在使用 Crank-Nicolson 方案进行完全离散化时采用了这些收敛率。结果表明,该方法在能量型规范中以 O(τ2+hk+1) 的阶次收敛,在 L2 规范中以 O(τ2+hk+2) 的阶次收敛。所报告的方法得到了一系列计算测试的支持,包括线性、半线性和 Allen-Cahn 模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Mathematics and Computers in Simulation
Mathematics and Computers in Simulation 数学-计算机:跨学科应用
CiteScore
8.90
自引率
4.30%
发文量
335
审稿时长
54 days
期刊介绍: The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
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