虚元法

IF 16.3 1区数学 Q1 MATHEMATICS

Acta Numerica Pub Date : 2023-05-01 DOI:10.1017/S0962492922000095

L. Beirão Da Veiga, F. Brezzi, L. D. Marini, A. Russo

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引用次数: 0

摘要

本综述有几个目的。它的主要目的是给出虚元方法(virtual element methods, VEMs)的一般特征的概念，这种方法是大约十年前在偏微分方程数值方法领域引入的，目的是允许将计算域分解成非常一般形状的多边形或多面体。尽管如此，这篇论文也是写给那些已经听说过(可能读过)虚拟机械设备，并有兴趣获得更精确信息的读者的，特别是关于它们在特定子领域的应用，如${C}^1$ -板弯曲问题的近似或固体和流体力学问题的近似。

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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The virtual element method

The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape. Nonetheless, the paper is also addressed to readers who have already heard (and possibly read) about VEMs and are interested in gaining more precise information, in particular concerning their application in specific subfields such as ${C}^1$ -approximations of plate bending problems or approximations to problems in solid and fluid mechanics.

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来源期刊

Acta Numerica MATHEMATICS-

CiteScore

26.00

自引率

0.70%

发文量

期刊介绍： Acta Numerica stands as the preeminent mathematics journal, ranking highest in both Impact Factor and MCQ metrics. This annual journal features a collection of review articles that showcase survey papers authored by prominent researchers in numerical analysis, scientific computing, and computational mathematics. These papers deliver comprehensive overviews of recent advances, offering state-of-the-art techniques and analyses. Encompassing the entirety of numerical analysis, the articles are crafted in an accessible style, catering to researchers at all levels and serving as valuable teaching aids for advanced instruction. The broad subject areas covered include computational methods in linear algebra, optimization, ordinary and partial differential equations, approximation theory, stochastic analysis, nonlinear dynamical systems, as well as the application of computational techniques in science and engineering. Acta Numerica also delves into the mathematical theory underpinning numerical methods, making it a versatile and authoritative resource in the field of mathematics.