Design and performance of a space–time virtual element method for the heat equation on prismatic meshes

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.