In this study, we investigate a hybrid-type anisotropic weakly over-penalised symmetric interior penalty method for the Poisson equation on convex domains. Compared with the well-known hybrid discontinuous Galerkin methods, our approach is simple and easy to implement. Our primary contributions are the proposal of a new scheme and the demonstration of a proof for the consistency term, which allows us to estimate the anisotropic consistency error. The key idea of the proof is to apply the relation between the Raviart--Thomas finite element space and a discontinuous space. In numerical experiments, we compare the calculation results for standard and anisotropic mesh partitions.

翻译：本研究针对凸区域上的泊松方程，提出了一种混合型各向异性弱超罚对称内罚方法。与经典的混合间断伽辽金方法相比，本文方法结构简洁且易于实现。我们的主要贡献在于提出了一种新格式，并给出了相容性项的证明，这使得各向异性相容误差的估计成为可能。证明的核心思想在于利用Raviart--Thomas有限元空间与间断空间之间的关系。在数值实验中，我们对比了标准网格与各向异性网格划分下的计算结果。