论文标题
$ l^\ infty $ norm误差估计用于应用于泊松方程的HDG方法，并应用于DIRICHLET边界控制问题
$L^\infty$ norm error estimates for HDG methods applied to the Poisson equation with an application to the Dirichlet boundary control problem
论文作者
论文摘要
我们证明，通过标准的可杂交不连续的Galerkin（HDG）方法，我们证明了准最佳$ l^\ ind $ norm误差估计（最多为对数因素），以解决Poisson问题。尽管此类估计值可用于符合和混合有限元方法，但这是HDG的第一个证明。该方法的动机是由已知的$ l^\ infty $ norm估算的混合元素估计。我们展示了两个应用：第一个是为了证明边界通量估计值的最佳收敛速率，其次是证明，在理论上可以预期的是，数值观察到的dirichlet边界控制问题解决方案的收敛速率。数值示例表明，实际上可以看到预测率。
We prove quasi-optimal $L^\infty$ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming and mixed finite element methods, this is the first proof for HDG. The method of proof is motivated by known $L^\infty$ norm estimates for mixed finite elements. We show two applications: the first is to prove optimal convergence rates for boundary flux estimates, and the second is to prove that numerically observed convergence rates for the solution of a Dirichlet boundary control problem are to be expected theoretically. Numerical examples show that the predicted rates are seen in practice.
