We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness and to obtain a priori error estimates, our space-time HDG formulation makes use of weighted inner products. We perform an a priori error analysis in which the dependence on the time step and spatial mesh size is explicit. The analysis results are supported by numerical examples.

中文翻译：

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线性自由表面波的时空可混合不连续Galerkin方法

我们提出并分析了一种新颖的时空可杂交不连续Galerkin（HDG）方法，用于棱形时空网格上的线性自由表面问题。我们考虑了一种混合公式，该公式可以立即使我们计算流体的速度。为了显示正确的姿势并获得先验误差估计，我们的时空HDG公式使用了加权内积。我们执行先验误差分析，其中对时间步长和空间网格大小的依赖性是明确的。数值实例支持了分析结果。