The symmetric 0 interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selection of the involved stability parameter in terms of the geometry of the underlying triangulation for arbitrary polynomial degrees. The proposed choice ensures a stable discretization with guaranteed discrete ellipticity constant. Numerical evidence for uniform and adaptive mesh-refinement and various polynomial degrees supports the reliability and efficiency of the local parameter selection and recommends this in practice. The approach is documented in 2D for triangles, but the methodology behind can be generalized to higher dimensions, to non-uniform polynomial degrees, and to rectangular discretizations. An appendix presents the realization of our proposed parameter selection in various established finite element software packages. a detailed documentation of C0 interior penalty method in.

中文翻译：

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双调和方程C0内罚法中的局部参数选择

对称的0内罚法是双调和方程最流行的间断伽辽金方法之一。本文介绍了根据任意多项式次数的基础三角测量的几何形状自动局部选择所涉及的稳定性参数。所提出的选择确保了稳定的离散化和有保证的离散椭圆率常数。均匀和自适应网格细化以及各种多项式次数的数值证据支持局部参数选择的可靠性和效率，并在实践中推荐这样做。该方法以三角形的二维形式记录，但背后的方法可以推广到更高的维度、非均匀多项式次数和矩形离散化。附录介绍了我们在各种已建立的有限元软件包中建议的参数选择的实现。C 的详细文档0内惩罚法.