We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and locally efficient. In the reliability analysis we combine a Peclet-robust coercivity type result and a saturation assumption, while local efficiency analysis is based on using bubble functions. The analysis considers both local space and time adaptivity and is verified by numerical simulations on problems which include boundary and interior layers.

翻译：本文提出并分析了一种针对时间依赖对流-扩散问题的时空杂交间断伽辽金离散化的后验误差估计子。该基于残差的误差估计子被证明是可靠且局部有效的。在可靠性分析中，我们结合了佩克莱特鲁棒型强制结果和饱和假设，而局部效率分析则基于气泡函数的使用。分析同时考虑了局部空间和时间自适应性，并通过包含边界层和内层的数值模拟进行了验证。