An a-posteriori error estimate for h p -adaptive DG methods for convection-diffusion problems on anisotropically refined meshes
An a-posteriori error estimate for h p -adaptive DG methods for convection-diffusion problems on anisotropically refined meshes
复制标题
各向异性细化网格上对流扩散问题的 HP 自适应 DG 方法的后验误差估计
DOI：
10.1016/j.camwa.2012.10.015
复制
发表时间：
2014
影响因子：
2.9
通讯作者：
Giani S
中科院分区：
文献类型：
--
作者：
Giani S
我们证明了 h p 自适应不连续伽辽金方法的后验误差估计，用于各向异性细化矩形单元上对流扩散方程的数值解。该估计产生根据与扩散相关的自然范数和与对流相关的半范数测量的误差的全局上限和下限。底层网格的各向异性通过对齐措施合并到上限中。我们提出了一系列数值实验来测试这种方法在全自动 HP 自适应细化算法中的可行性。
We prove an a-posteriori error estimate for h p-adaptive discontinuous Galerkin methods for the numerical solution of convection–diffusion equations on anisotropically refined rectangular elements. The estimate yields global upper and lower bounds of the errors measured in terms of a natural norm associated with diffusion and a semi-norm associated with convection. The anisotropy of the underlying meshes is incorporated in the upper bound through an alignment measure. We present a series of numerical experiments to test the feasibility of this approach within a fully automated h p-adaptive refinement algorithm.