In this work, we derive a posteriori error estimates for discontinuous Galerkin finite element method on polytopal mesh. We construct a reliable and efficient a posteriori error estimator on general polygonal or polyhedral meshes. An adaptive algorithm based on the error estimator and DG method is proposed to solve a variety of test problems. Numerical experiments are performed to illustrate the effectiveness of the algorithm.

中文翻译：

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多面体网格上不连续Galerkin有限元方法的后验误差估计

在这项工作中，我们得出了多面体网格上不连续Galerkin有限元方法的后验误差估计。我们在一般的多边形或多面体网格上构造了可靠而有效的后验误差估计器。提出了一种基于误差估计和DG方法的自适应算法，以解决各种测试问题。数值实验表明了该算法的有效性。