论文标题
至高无上
Supremum-norm a posteriori error control of quadratic discontinuous Galerkin methods for the obstacle problem
论文作者
论文摘要
对于椭圆障碍问题的二次不连续的盖尔金方法，我们对近亲范围的高规范进行后验误差分析。我们定义了两个离散集（由GADDAM，GUDI和KAMANA [1]动机），一组具有积分约束，另一组在正交点处具有淋巴结约束，并讨论了拟议的后验误差估计器的点上的可靠性和效率。在分析中，我们采用线性平均函数将DG有限元空间传递到标准符合有限元元素空间，并利用泊松问题的绿色功能上的尖锐边界。此外，通过适当修改离散溶液的符合部分uh构建与连续溶液U相对应的上屏障和下部屏障函数。最后，提出了数值实验以补充理论结果。
We perform a posteriori error analysis in the supremum norm for the quadratic discontinuous Galerkin method for the elliptic obstacle problem. We define two discrete sets (motivated by Gaddam, Gudi and Kamana [1]), one set having integral constraints and other one with the nodal constraints at the quadrature points, and discuss the pointwise reliability and efficiency of the proposed a posteriori error estimator. In the analysis, we employ a linear averaging function to transfer DG finite element space to standard conforming finite element space and exploit the sharp bounds on the Green's function of the Poisson's problem. Moreover, the upper and the lower barrier functions corresponding to continuous solution u are constructed by modifying the conforming part of the discrete solution uh appropriately. Finally, numerical experiments are presented to complement the theoretical results.
