We introduce a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations. The proposed method is based on a coarse grid and iteratively improves the solution's accuracy by solving local elliptic problems in refined subdomains. For purely diffusion problems, we already proved that this scheme converges under minimal regularity assumptions [A. Abdulle and G.Rosilho de Souza, ESAIM: M2AN, 53(4):1269--1303, 2019]. In this paper, we provide an algorithm for the automatic identification of the local elliptic problems' subdomains employing a flux reconstruction strategy. Reliable error estimators are derived for the local adaptive method. Numerical comparisons with a classical nonlocal adaptive algorithm illustrate the efficiency of the method.

翻译：我们引入了局部适应性不连续的Galerkin方法,用于对流扩散反应方程式。拟议方法基于粗粗的网格,通过解决精细子域的局部椭圆性问题,反复地提高解决方案的准确性。对于纯粹的扩散问题,我们已经证明,这一方法在最低常规假设[A. Abdulle和G. Rosilho de Souza, ESAM: M2AN, 53(4):1269-1303, 20199] 下集。在本文中,我们提供了一种算法,用于利用流动重建战略自动识别本地的椭圆性问题子域。可靠的误差估计器是用于本地适应方法的。与传统的非本地适应性算法的数值比较显示了该方法的效率。