极弱有限元方法：离散化与应用

IF 1.5 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Engineering Computations Pub Date : 2024-03-22 DOI:10.1108/ec-10-2023-0699

Douglas Ramalho Queiroz Pacheco

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引用次数: 0

摘要

研究结果提出并测试了各种符合要求的离散方法，数值结果表明不同类型的问题都具有良好的准确性和稳定性。原创性/价值这是首批提出并测试基元形式的极弱变分公式具体离散方法的文章之一。数值结果（包括一个基于真实磁共振成像数据的问题）表明，极弱有限元方法具有处理低正则性问题的潜力。

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Very weak finite element methods: discretisation and applications

Purpose

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

Design/methodology/approach

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Findings

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

Originality/value

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

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来源期刊

Engineering Computations 工程技术-工程：综合

CiteScore

3.40

自引率

6.20%

发文量

审稿时长

5 months

期刊介绍： The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm