We present a posteriori error analysis in the supremum norm for the symmetric interior penalty discontinuous Galerkin method for the elliptic obstacle problem. We construct discrete barrier functions based on appropriate corrections of the conforming part of the solution that is obtained via a constrained averaging operator. The corrector function accounts properly for the non-conformity of the approximation and it is estimated by direct use of the Green's function of the unconstrained elliptic problem. The use of the continuous maximum principle guarantees the validity of the analysis without mesh restrictions but shape regularity. The proposed residual type estimators are shown to be reliable and efficient. Numerical results in two dimensions are included to verify the theory and validate the performance of the error estimator.
翻译:在对称内刑不连续加勒金法对椭圆障碍问题进行对称内罚的超前误差规范中,我们提出事后误差分析。我们根据对通过受限平均操作员获得的解决方案符合部分的适当校正,建立离散障碍功能。正确函数恰当地说明了近似不相符之处,并通过直接使用Green对未受限制的椭圆问题的功能来估计。使用连续最高原则保证分析的有效性,不设网目限制,但形成规律性。拟议的剩余类型估计仪显示是可靠和有效的。数字结果包括两个方面,以核实误差估计仪的理论和性能。