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：本文提出了一种用于热传导方程离散化的时空虚拟元方法，该方法定义于一般棱柱网格上，并具备可变精度阶次。我们讨论了有效处理时空网格结构的策略。针对光滑解与奇异解情形，对所提方法的h-型与hp-型版本进行了收敛性测试，并验证了基于残差型误差指示器的时空自适应网格细化方法。