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：我们建议并分析一个时空虚拟元素方法,用于在标准Petrov-Galerkin配方制基础上将时空气瓶中的热方程式分解。当地离散函数是多元数据热方程式问题的解决办法。全球虚拟元素空间与空间不兼容,因此该方法的分析和设计独立于空间层面。时间板之间的信息通过对离散函数进行多角度预测的上风条件传输。我们证明这个方案是完善的,也是最佳的误差估计,并用数测试来验证它们。