弯曲扇形区域弹性方程的鲁棒映射谱方法

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-01-16 DOI:10.1016/j.apnum.2025.01.008

Yuling Guo , Zhongqing Wang , Chao Zhang

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引用次数: 0

摘要

本文引入了一种鲁棒映射Legendre谱- galerkin方法，用于求解具有弯曲边界的单连通扇形区域的弹性问题。通过极坐标变换，将扇形域映射到矩形上，将原弹性方程转化为变系数方程。然后，我们为这个变系数方程建立了一个勒让德谱-伽辽金格式。此外，我们还证明了当lam系数λ保持有界时，数值解在h1范数下的最优收敛性。数值例子表明，即使λ接近无穷大，我们的方法也具有很高的精度和鲁棒性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A robust mapping spectral method for elastic equations in curved fan-shaped domains

In this paper, we introduce a robust mapping Legendre spectral-Galerkin method for addressing elastic problems in simply-connected, fan-shaped domains with curved boundaries. By employing a polar coordinate transformation, we map the fan-shaped domain onto a rectangle, which transforms the original elastic equation into a variable coefficient equation. We then develop a Legendre spectral-Galerkin scheme for this variable coefficient equation. Additionally, we demonstrate the optimal convergence of the numerical solution in the

H^{1}

-norm as the Lamé coefficient λ remains bounded. Numerical examples illustrate the high accuracy and robustness of our method, even as λ approaches infinity.

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来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.