A local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations is introduced. Departing from classical adaptive algorithms, the proposed method is based on a coarse grid and iteratively improves the accuracy of the solution by solving local elliptic problems identified by an a posteriori error control. Based on a flux reconstruction strategy, a posteriori error estimators free of undetermined constants for such a scheme are derived. Numerical comparison with a classical adaptive algorithm illustrate the efficiency and robustness of the new method.
翻译：采用了局部适应性不连续的 Galerkin 方法, 用于对流- 扩散- 反应方程式。 从传统的适应性算法中分离出, 提议的方法基于粗糙的网格, 并通过事后误差控制解决本地的椭圆问题, 反复提高解决方案的准确性。 根据通量重建战略, 得出了一个后端误差估计器, 且该方法没有不确定的常数。 与传统的适应性算法进行数值比较, 显示了新方法的效率和稳健性 。
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