Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

中文翻译：

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用于二阶椭圆问题的内部惩罚族可混合不连续伽辽金方法

摘要 本文的重点是分析二阶椭圆问题的可混合内罚不连续伽辽金方法族。我们推导出能量范数中的先验误差估计，这些估计对于网格大小是最佳的。证明了次优 L2 范数误差估计。这些结果在两个和三个维度上都是有效的。数值结果支持我们的理论发现，我们说明了该方法的计算成本。