This work is concerned with adaptive hybridizable discontinuous Galerkin methods of nonstationary convection diffusion problems. We address first the spatially semidiscrete case and then move to the fully discrete scheme by introducing a backward Euler discretization in time. More specifically, the computable a posteriori error estimator for the time-dependent problem is obtained by using the idea of elliptic reconstruction and conforming-nonconforming decomposition. In view of the method that has been employed in the time-dependent problem, we also obtain a computable a posteriori error estimator for the fully discrete scheme. Finally, two examples show the performance of the obtained a posteriori error estimators.

中文翻译：

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非平稳对流扩散问题的自适应可混合不连续Galerkin方法

这项工作涉及非平稳对流扩散问题的自适应可杂交不连续伽勒金方法。我们首先解决空间上半离散的情况，然后通过及时引入反向欧拉离散化而转向完全离散的方案。更具体地，通过使用椭圆重构和一致非一致性分解的思想，获得了与时间有关的问题的可计算后验误差估计器。鉴于已在与时间有关的问题中采用的方法，我们还为完全离散方案获得了可计算的后验误差估计器。最后，两个例子说明了所获得的后验误差估计器的性能。