对流扩散问题的时空可杂交间断Galerkin方法的后验误差分析
A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem
AI总结：
本文为时间依赖对流扩散问题的时空HDG离散构造基于残差的后验误差估计子，证明其可靠性与局部效率，并通过含边界层和内部层的数值实验验证。
AI中文摘要：
我们针对时间依赖对流扩散问题的时空可杂交间断Galerkin离散，提出并分析了一种后验误差估计子。该基于残差的误差估计子被证明是可靠且局部高效的。在可靠性分析中，我们结合了对Peclet数稳健的强制性型结果与饱和假设，而局部效率分析则基于使用泡函数。该分析同时考虑了局部空间和时间自适应性，并通过在包含边界层和内部层的问题上进行数值模拟得到验证。
英文摘要：
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.
