多边形网格上非线性变阶时间分数扩散方程的两网格虚元法

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-10-03 DOI:10.1080/00207160.2023.2263589

Qiling Gu, Yanping Chen, Jianwei Zhou, Yunqing Huang

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引用次数: 0

摘要

摘要本文建立了一种求解多边形网格上非线性变阶时间分数扩散方程的双网格虚元法。在时间方向上考虑L1梯度网格格式，在空间方向上采用VEM近似。双网格虚元算法将细网格上的非线性时间分数问题的解简化为在同一细网格上的一个线性方程和在更粗网格上的一个原始非线性问题的解。因此，我们的算法不仅节省了总计算成本，而且保持了最优的精度。详细分析了该方案和相应的双网格方案的最优L2误差估计。最后，通过数值实验验证了理论结果。关键词:虚元法非线性变阶分数方程双网格多边形网格先验误差估计数学学科分类:65M6065N3034K3765M1565M55披露声明作者未报告潜在利益冲突。基金资助:国家自然科学基金国家重点项目[批准号:11931003]、国家自然科学基金[批准号:41974133]、湖南省研究生创新基金[批准号:XDCX2021B098]、湖南省研究生科研创新项目[批准号:CX20210597]。

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A two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes

AbstractIn this paper, we develop a two-grid virtual element method for nonlinear variable-order time-fractional diffusion equation on polygonal meshes. The L1 graded mesh scheme is considered in the time direction, and the VEM is used to approximate spatial direction. The two-grid virtual element algorithm reduces the solution of the nonlinear time fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithm not only saves total computational cost, but also maintains the optimal accuracy. Optimal L2 error estimates are analysed in detail for both the VEM scheme and the corresponding two-grid VEM scheme. Finally, numerical experiments presented confirm the theoretical findings.Keywords: Virtual element methodnonlinearvariable-order fractional equationtwo-gridpolygonal meshesa priori error estimateMathematics subject classifications: 65M6065N3034K3765M1565M55 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work is supported by the State Key Program of National Natural Science Foundation of China [grant number 11931003] and National Natural Science Foundation of China [grant number 41974133], Hunan Provincial Innovation Foundation for Postgraduate, China [grant number XDCX2021B098], Postgraduate Scientific Research Innovation Project of Hunan Province [grant number CX20210597].

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

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