论文标题
$ c^0 $内部惩罚方法中的本地参数选择
Local parameter selection in the $C^0$ interior penalty method for the biharmonic equation
论文作者
论文摘要
对称$ C^0 $内部惩罚方法是Biharmonic方程最受欢迎的不连续的Galerkin方法之一。本文根据任意多项式度的基础三角剖分的几何形状，引入了涉及稳定性参数的自动局部选择。提出的选择可确保稳定的离散化，并保证离散椭圆度常数。均匀和适应性网格再插入和各种多项式学位的数值证据支持局部参数选择的可靠性和效率，并在实践中建议这样做。该方法在三角形中记录在2D中，但是背后的方法可以推广到更高的维度，非均匀的多项式程度和矩形离散化。两个附录介绍了我们在各种已建立的有限元软件软件包中实现我们提出的参数选择，以及用于最低级$ C^0 $内部惩罚方法的自包含MATLAB程序的详细文档。
The symmetric $C^0$ 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. Two appendices present the realization of our proposed parameter selection in various established finite element software packages as well as a detailed documentation of a self-contained MATLAB program for the lowest-order $C^0$ interior penalty method.
