A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-05-17 DOI:10.1090/mcom/3843

Dianming Hou, Lili Ju, Zhonghua Qiao

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引用次数: 0

Abstract

In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is carefully constructed based on the combination of first and second-order backward differentiation formulas with nonuniform time steps for temporal approximation and the central finite difference for spatial discretization. The discrete maximum bound principle is proved of the proposed scheme by using the kernel recombination technique under certain mild constraints on the time steps and the ratios of adjacent time step sizes. Furthermore, we rigorously derive the discrete H 1 H^{1} error estimate and energy stability for the classic constant mobility case and the L ∞ L^{\infty } error estimate for the general mobility case. Various numerical experiments are also presented to validate the theoretical results and demonstrate the performance of the proposed method with a time adaptive strategy.

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具有一般迁移率的Allen-Cahn方程的线性二阶最大界保原理BDF格式

本文提出并分析了求解具有一般迁移率的Allen-Cahn方程的一种线性二阶数值方法。提出的全离散格式是基于一阶和二阶后向微分公式的组合，时间近似采用非均匀时间步长，空间离散采用中心有限差分。在一定的时间步长和相邻时间步长之比的温和约束下，利用核重组技术证明了该方案的离散最大界原理。在此基础上，我们严格推导了经典常迁移情况下的离散H∞H^{1}误差估计和能量稳定性，以及一般迁移情况下的L∞L^ {\infty误差估计。各种数值实验验证了理论结果，并证明了采用时间自适应策略的方法的性能。}

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.