非稳态布尔格斯方程的克兰克-尼科尔森有限元求解系数向量的降维方法

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-11-05 DOI:10.1016/j.jmaa.2024.129031

Chunxia Huang, Hong Li, Baoli Yin

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引用次数: 0

摘要

本文主要关注使用 Crank-Nicolson FE（CNFE）方法求解的非稳态伯格斯方程的有限元（FE）解系数向量的降维问题。适当的正交分解（POD）基础由快照矩阵构建，快照矩阵由前 L 个解形成，其中 L 明显小于 CNFE 方法的总时间步数 N。通过重构 CNFE 方法的矩阵形式，提出了一种降维 Crank-Nicolson 有限元（RDCNFE）方法，并讨论了稳定性分析和误差估计。通过数值试验验证了理论结果，并证明了 RDCNFE 方法的高效性。

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A reduced-dimension method of Crank-Nicolson finite element solution coefficient vectors for the unsteady Burgers equation

This paper primarily focuses on the dimensionality reduction of finite element (FE) solution coefficient vectors for the unsteady Burgers equation, solved using the Crank-Nicolson FE (CNFE) method. The proper orthogonal decomposition (POD) basis is constructed from the snapshot matrix, which is formed using the first L solutions, where L is significantly smaller than the total number of time steps N of the CNFE method. By reconstructing the matrix form of the CNFE method, a reduced-dimension Crank-Nicolson finite element (RDCNFE) method is proposed and stability analysis and error estimates are discussed. Numerical tests are implemented to verify the theoretical results and demonstrate the high efficiency of the RDCNFE method.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.