Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes
Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes
复制标题
任意层悬挂节点网格上不连续伽辽金有限元近似的完全可计算误差界
DOI：
10.1137/080725945
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发表时间：
2010
影响因子：
2.9
通讯作者：
Ainsworth M
中科院分区：
文献类型：
--
作者：
Ainsworth M
我们得到了一阶对称内罚Galerkin（SIPG）、非对称内罚Galerkin（NIPG）、不完全内罚Galerkin（IIPG）有限元近似的线性二阶椭圆问题的网格包含任意数量的水平悬挂节点和组成三角形元素估计是完全免费的未知常数，并提供有保证的数值界上的破碎的能量和DG-范数的错误。这些估计还示出，提供了一个下界的破碎的能量的误差和DG-范数的常数和高阶数据振荡项。我们还获得了一个明确的可计算的内部惩罚参数的值，以确保存在的不连续Galerkin有限元逼近的所有版本的方法。
We obtain fully computable a posteriori error bounds on the broken energy seminorm and discontinuous Galerkin norm (DG-norm) of the error in first order symmetric interior penalty Galerkin (SIPG), nonsymmetric interior penalty Galerkin (NIPG), and incomplete interior penalty Galerkin (IIPG) finite element approximations of a linear second order elliptic problem on meshes containing an arbitrary number of levels of hanging nodes and comprised of triangular elements. The estimators are completely free of unknown constants and provide guaranteed numerical bounds on the broken energy seminorm and DG-norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and DG-norm of the error up to a constant and higher order data oscillation terms. We also obtain an explicit computable bound for the value of the interior penalty parameter needed to ensure the existence of the discontinuous Galerkin finite element approximation for all versions of the method.