无需执行[数学]元素即可计算[数学]符合有限元近似值

IF 3 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Scientific Computing Pub Date : 2024-07-22 DOI:10.1137/23m1615486

Mark Ainsworth, Charles Parker

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引用次数: 0

摘要

SIAM 科学计算期刊》，第 46 卷第 4 期，第 A2398-A2420 页，2024 年 8 月。摘要。我们开发了一种计算平面四阶椭圆问题的[math]拟合有限元近似的方法，而无需实现[math]元素。该算法包括用只需要[math]-conform Poisson 类型求解的预处理和后处理步骤取代原始的[math]-conform 方案，以及只需要最多[math]-conformity 的内斯托克斯问题。然后，我们通过三个数值示例演示了该方法在摩根-斯科特元素中的应用。计算结果的可重复性。本文被授予 "SIAM 可重现徽章"：代码和数据可用"，以表彰作者遵循了 SISC 和科学计算界重视的可重现性原则。读者可通过 https://doi.org/10.5281/zenodo.10070565 获取代码和数据，以重现本文中的结果。

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Computing [math]-Conforming Finite Element Approximations Without Having to Implement [math]-Elements

SIAM Journal on Scientific Computing, Volume 46, Issue 4, Page A2398-A2420, August 2024.
Abstract. We develop a method to compute the [math]-conforming finite element approximation to planar fourth order elliptic problems without having to implement [math] elements. The algorithm consists of replacing the original [math]-conforming scheme with preprocessing and postprocessing steps that require only an [math]-conforming Poisson type solve and an inner Stokes-like problem that again only requires at most [math]-conformity. We then demonstrate the method applied to the Morgan–Scott elements with three numerical examples. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://doi.org/10.5281/zenodo.10070565.

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来源期刊

SIAM Journal on Scientific Computing 数学-应用数学

CiteScore

5.50

自引率

3.20%

发文量

209

审稿时长

1 months

期刊介绍： The purpose of SIAM Journal on Scientific Computing (SISC) is to advance computational methods for solving scientific and engineering problems. SISC papers are classified into three categories: 1. Methods and Algorithms for Scientific Computing: Papers in this category may include theoretical analysis, provided that the relevance to applications in science and engineering is demonstrated. They should contain meaningful computational results and theoretical results or strong heuristics supporting the performance of new algorithms. 2. Computational Methods in Science and Engineering: Papers in this section will typically describe novel methodologies for solving a specific problem in computational science or engineering. They should contain enough information about the application to orient other computational scientists but should omit details of interest mainly to the applications specialist. 3. Software and High-Performance Computing: Papers in this category should concern the novel design and development of computational methods and high-quality software, parallel algorithms, high-performance computing issues, new architectures, data analysis, or visualization. The primary focus should be on computational methods that have potentially large impact for an important class of scientific or engineering problems.