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 $\mathcal{O}(1/h^{1+\delta})$, where $h$ denotes the mesh size and $\delta$ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity, and boundedness (with $h^{\delta}$-dependency), and we derive updated error estimates for both discrete energy- and $L^{2}$-norms. All theoretical results are supported by numerical evidence.
翻译:在本文中,我们用二等省略问题可变处罚办法,对混合内刑不连续的Galerkin(H-IP)家庭进行了改进的先验误差估计,其策略是使用美元(mathcal{O})(1/h ⁇ 1 ⁇ ⁇ delta})形式的惩罚功能,即以美元表示网状大小,美元和德尔塔美元是一个依赖用户的参数。然后,我们用数量证据来量化其对趋同分析的直接影响,即(强)一致性、离散的共性、约束性(与$h ⁇ delta}美元相依性),我们得出的是离散能源的最新误差估计值和$L ⁇ 2}-norms的最新误差估计值。所有理论结果都得到数字证据的支持。