论文标题
改善了对高度各向异性扩散问题的可变惩罚的杂交内部惩罚方法的改进误差估计
Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems
论文作者
论文摘要
在本文中，我们通过使用二阶椭圆问题的可变惩罚来提出对杂交内部罚款不连续的Galerkin（H-IP）方法的先验误差估计。该策略是使用$ \ MATHCAL {O}（1/H^{1+δ}）$的惩罚功能，其中$ h $表示网格大小，$δ$是用户依赖的参数。然后，我们量化了其对收敛分析的直接影响，即（强）一致性，离散的强制性和有限性（具有$ H^δ$依赖性），并且我们得出了离散能量和$ l^{2} $的更新错误估计。误差分析的独创性特别依赖于精确解决方案的构型插值剂的使用。所有理论结果都由数值证据支持。
In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form $\mathcal{O}(1/h^{1+δ})$, where $h$ denotes the mesh size and $δ$ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity, and boundedness (with $h^δ$-dependency), and we derive updated error estimates for both discrete energy- and $L^{2}$-norms. The originality of the error analysis relies specifically on the use of conforming interpolants of the exact solution. All theoretical results are supported by numerical evidence.
