论文标题
加热方程的时空虚拟元素
Space-time virtual elements for the heat equation
论文作者
论文摘要
我们根据标准的Petrov-Galerkin公式提出并分析了一种时空虚拟元素方法，用于在时空缸中离散热方程。局部离散功能是与多项式数据的热方程问题的解决方案。全局虚拟元素空间在空间中不合格，因此该方法的分析和设计与空间维度无关。时间板之间的信息是通过涉及离散函数多项式投影的上风术语传输的。我们证明了该方案的良好姿势和最佳误差估计，并通过几个数值测试对其进行验证。
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.
