论文标题
莫利元件在一般多地分区上使用弱彩色方法的扩展
An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods
论文作者
论文摘要
本文介绍了众所周知的莫利元素用于Biharmonic方程，并使用弱Galerkin有限元方法将其应用从三角元素扩展到一般的多面元素。通过利用Schur的补充，弱Galerkin方法的补充，该扩展不仅保留了与三角元素上的Morley元素相同的自由度，而且还将其适用性扩展到了一般多年元素上。数值方案是通过局部构建弱切向导数和弱二阶偏导数来设计的。数值近似的错误估计均在能量规范和$ l^2 $规范中建立。进行了一系列数值实验以验证理论发展。
This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements using the weak Galerkin finite element methods. By leveraging the Schur complement of the weak Galerkin method, this extension not only preserves the same degrees of freedom as the Morley element on triangular elements but also expands its applicability to general polytopal elements. The numerical scheme is devised by locally constructing weak tangential derivatives and weak second-order partial derivatives. Error estimates for the numerical approximation are established in both the energy norm and the $L^2$ norm. A series of numerical experiments are conducted to validate the theoretical developments.
