In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant depends linearly on the finite element mesh parameter, but in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings.

翻译：本文分析了用于时间依赖偏微分方程时空离散化的修正希尔伯特变换的离散inf-sup条件及相关误差估计。结果表明，稳定性常数与有限元网格参数呈线性相关，但在大多数情况下，我们能够证明最优收敛性。我们通过一系列数值实验来验证理论结果。