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.

中文翻译：

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热方程的时空虚拟单元

SIAM 数值分析杂志，第 62 卷，第 1 期，第 199-228 页，2024 年 2 月。
摘要。我们基于标准 Petrov-Galerkin 公式，提出并分析了一种时空虚拟元方法，用于时空圆柱体中热方程的离散化。局部离散函数是具有多项式数据的热方程问题的解。全局虚拟元空间在空间上是不相容的，因此该方法的分析和设计与空间维度无关。时间片之间的信息通过涉及离散函数的多项式投影的逆风项来传输。我们证明了该方案的适定性和最优误差估计，并通过多次数值测试对其进行验证。