论文标题
多边形网格上完全离散的Div-div复合物的偶然性
A serendipity fully discrete div-div complex on polygonal meshes
论文作者
论文摘要
在这项工作中，我们解决了离散弹性复合物的面部自由度（DOF）的降低。具体而言，使用偶然性技术，我们开发了由三维弹性复合物的痕迹引起的最近引入的二维复合物的简化版本。还原过程的基石是根据边界值的对称张量值多项式场的新估计值，并以适当的内部值的适当投影完成。我们证明了原始复合物的一系列新结果，并表明还原的复合物具有与原始综合性相同的同源性和分析性能。本文还包含一个附录，其中包含Poincaré通用的证据 - 混合领域的Korn型不平等。
In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate of symmetric tensor-valued polynomial fields in terms of boundary values, completed with suitable projections of internal values for higher degrees. We prove an extensive set of new results for the original complex and show that the reduced complex has the same homological and analytical properties as the original one. This paper also contains an appendix with proofs of general Poincaré--Korn-type inequalities for hybrid fields.
