四阶div问题的梯度一致性谱元法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-02-24 DOI:10.1016/j.cam.2025.116599

Yang Han , Ping Lin , Lixiu Wang , Qian Zhang

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引用次数: 0

摘要

本文介绍了一种利用梯度一致性谱元在立方体网格上求解四阶微分问题的新数值方法。首先确定梯度一致性谱元的连续性要求，然后利用广义雅可比多项式和Piola变换构造这些谱元。所得到的基函数表现出层次结构，使它们易于扩展到更高阶。将这些符合梯度的谱元应用于求解四阶微分问题，并给出数值算例验证了该方法的有效性和有效性。

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Graddiv-conforming spectral element method for fourth-order div problems

This paper introduces a novel numerical method to solve fourth-order div problems using

graddiv

-conforming spectral elements on cuboidal meshes. We start by determining the continuity requirements for

graddiv

-conforming spectral elements, followed by constructing these elements using generalized Jacobi polynomials and the Piola transformation. The resulting basis functions exhibit a hierarchical structure, making them easily extendable to higher orders. We apply these

graddiv

-conforming spectral elements to solve the fourth-order div problem and present numerical examples to verify both the efficiency and effectiveness of the method.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.