用直接不连续伽辽金公式求解Allen-Cahn方程的勒让德谱体积法

IF 2.9 2区 数学 Q1 MATHEMATICS, APPLIED
Chaoyue Guan, Yuli Sun, Jing Niu
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引用次数: 0

摘要

本文引入了一类新的求解Allen-Cahn方程的Legendre谱体积(LSV)方法。每个光谱体积(SV)用k个高斯-勒让德点进行细化,以定义任意阶控制体积(CV)。此外,采用直接不连续伽辽金(DDG)方法处理二阶导数。此外,还详细介绍了具有Neumann和周期边界条件的一维和二维Allen-Cahn方程的四个数值实验。这些实验证明了该方法在捕获相变方面的稳定性和准确性。同时,我们还证明了LSV方法可以保持能量耗散和均匀有界等物理性质。值得注意的是,我们观察到LSV方法既能达到最优收敛,也能达到超收敛。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Legendre spectral volume methods for Allen–Cahn equations by the direct discontinuous Galerkin formula
In this paper, we introduce novel class of Legendre spectral volume (LSV) methods for solving Allen–Cahn equations. Each spectral volume (SV) is refined with k Gauss–Legendre points to define an arbitrary order control volume (CV). Moreover, the second derivative is handled using the direct discontinuous Galerkin (DDG) approach. Furthermore, four numerical experiments are detailed including 1D and 2D Allen–Cahn equations with Neumann and periodic boundary conditions. These experiments demonstrate the stability and accuracy in capturing phase transitions of the approach. Meanwhile, we also show the LSV methods can maintain physical properties such as energy dissipation and uniform boundedness. It is worth mentioning that we observe that the LSV methods achieve both optimal convergence and superconvergence as the numerical flux parameter is carefully selected.
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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