A novel space-time discretization for the (linear) scalar-valued dissipative wave equation is presented. It is a structured approach, namely, the discretization space is obtained tensorizing the Virtual Element (VE) discretization in space with the Discontinuous Galerkin (DG) method in time. As such, it combines the advantages of both the VE and the DG methods. The proposed scheme is implicit and it is proved to be unconditionally stable and accurate in space and time.

翻译：针对（线性）标量耗散波动方程，提出了一种新型时空离散化方法。该结构化方法将空间维度的虚拟单元法（VE）离散化与时间维度的间断伽辽金法（DG）进行张量积耦合，从而融合了VE与DG两种方法的优势。所提格式为隐式格式，经严格证明其在时空维度上具有无条件稳定性和精确性。