论文标题
对流扩散反应方程的局部自适应不连续的盖尔金方法的后验错误分析
A posteriori error analysis of a local adaptive discontinuous Galerkin method for convection-diffusion-reaction equations
论文作者
论文摘要
我们引入了一种局部自适应不连续的盖尔金方法，用于对流扩散反应方程。所提出的方法基于粗网格，并通过解决精制亚域中的局部椭圆问题来迭代地提高溶液的准确性。对于纯粹的扩散问题，我们已经证明了该方案在最小的规律性假设下收敛[A. Abdulle和G.Rosilho de Souza，Esaim：M2an，53（4）：1269---1303，2019]。在本文中，我们为使用通量重建策略自动识别局部椭圆问题的子域提供了一种算法。可靠的误差估计器是针对局部自适应方法得出的。与经典非局部自适应算法的数值比较说明了该方法的效率。
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.
