Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes
Constant free error bounds for nonuniform order discontinuous Galerkin finite-element approximation on locally refined meshes with hanging nodes
复制标题
DOI：
10.1093/imanum/drp025
复制
发表时间：
2011
影响因子：
2.1
通讯作者：
M. Ainsworth;Richard Rankin
中科院分区：
文献类型：
--
作者：
M. Ainsworth;Richard Rankin
本文给出了线性二阶椭圆问题在三角形单元网格上的非均匀多项式阶对称内罚Galerkin、非对称内罚Galerkin和不完全内罚Galerkin有限元逼近的间断能量误差和间断Galerkin（DG）范数的完全可计算的无常数后验误差界。该估计器完全不含未知常数，并提供了破缺能量半模和误差DG模的有保证的数值界。这些估计还示出了提供一个下界的破碎的能量的误差和DG范数的一个常数和高阶数据振荡项。
We obtain fully computable constant free a posteriori error bounds on the broken energy seminorm and the discontinuous Galerkin (DG) norm of the error for nonuniform polynomial order symmetric interior penalty Galerkin, nonsymmetric interior penalty Galerkin and incomplete interior penalty Galerkin finite-element approximations of a linear second-order elliptic problem on meshes containing 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 the DG norm of the error. These estimators are also shown to provide a lower bound for the broken energy seminorm and the DG norm of the error up to a constant and higher-order data oscillation terms.