热方程的时空虚拟元素

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-01-18 DOI:10.1137/22m154140x

Sergio Gomez, Lorenzo Mascotto, Andrea Moiola, Ilaria Perugia

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引用次数: 0

摘要

SIAM 数值分析期刊》第 62 卷第 1 期第 199-228 页，2024 年 2 月。摘要我们提出并分析了一种基于标准 Petrov-Galerkin 公式的时空虚拟元素方法，用于时空圆柱体中热量方程的离散化。局部离散函数是多项式数据热方程问题的解。全局虚拟元素空间在空间上是非对称的，因此该方法的分析和设计与空间维度无关。时间板块之间的信息是通过涉及离散函数多项式投影的上风项传递的。我们证明了该方案的假设性和最佳误差估计，并通过几个数值测试进行了验证。

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Space-Time Virtual Elements for the Heat Equation

SIAM Journal on Numerical Analysis, Volume 62, Issue 1, Page 199-228, February 2024.
Abstract. We propose and analyze a space-time virtual element method for the discretization of the heat equation in a space-time cylinder, based on a standard Petrov–Galerkin formulation. Local discrete functions are solutions to a heat equation problem with polynomial data. Global virtual element spaces are nonconforming in space, so that the analysis and the design of the method are independent of the spatial dimension. The information between time slabs is transmitted by means of upwind terms involving polynomial projections of the discrete functions. We prove well posedness and optimal error estimates for the scheme, and validate them with several numerical tests.

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.