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.

翻译：本文提出并分析了一种用于热方程在时空柱体中离散化的时空虚拟元方法，该方法基于标准的Petrov-Galerkin形式。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为非协调的，因此该方法的设计与分析不受空间维度影响。通过涉及离散函数多项式投影的上风格式实现时间层间的信息传递。我们证明了该格式的适定性和最优误差估计，并通过多个数值实验验证了结果。