We present a space-time virtual element method for the discretization of the heat equation, which is defined on general prismatic meshes and variable degrees of accuracy. Strategies to handle efficiently the space-time mesh structure are discussed. We perform convergence tests for the $h$- and $hp$-versions of the method in case of smooth and singular solutions, and test space-time adaptive mesh refinements driven by a residual-type error indicator.

翻译：我们提出了一种用于热方程离散化的时空虚拟元方法，该方法定义在一般棱柱网格上，并具有可变的精度阶数。讨论了高效处理时空网格结构的策略。针对光滑解和奇异性解的情况，我们对方法的$h$和$hp$版本进行了收敛性测试，并测试了由残差型误差指示器驱动的时空自适应网格细化。