论文标题
二维矢量laplacian的不合格的原始杂交有限元法
A nonconforming primal hybrid finite element method for the two-dimensional vector Laplacian
论文作者
论文摘要
我们基于原始原理，为二维矢量laplacian介绍了一种不合格的混合有限元方法，该原理已知构象的方法是不一致的。使用类似于用于稳定杂交不连续的盖尔金（HDG）方法的刑罚术语来确保一致性，该方法具有由于Brenner，Li和Sung [Math [Math]的精心选择的惩罚参数。 Comp。，76（2007），第573-595页。我们的方法适应任意高阶的元素，并且像HDG方法一样，可以使用静态冷凝有效地实现它。最低订单的情况恢复了Brenner，Cui，Li和Sung的$ P_1 $ -NONCON-NONCON-NONCONTING方法[Numer。 Math。，109（2008），第509-533页]，我们表明在适当的规律性假设下实现了高阶收敛。该分析使得由于近叶式的域名构成了角落奇点的域名，因此新的使用加权Sobolev空间。
We introduce a nonconforming hybrid finite element method for the two-dimensional vector Laplacian, based on a primal variational principle for which conforming methods are known to be inconsistent. Consistency is ensured using penalty terms similar to those used to stabilize hybridizable discontinuous Galerkin (HDG) methods, with a carefully chosen penalty parameter due to Brenner, Li, and Sung [Math. Comp., 76 (2007), pp. 573-595]. Our method accommodates elements of arbitrarily high order and, like HDG methods, it may be implemented efficiently using static condensation. The lowest-order case recovers the $P_1$-nonconforming method of Brenner, Cui, Li, and Sung [Numer. Math., 109 (2008), pp. 509-533], and we show that higher-order convergence is achieved under appropriate regularity assumptions. The analysis makes novel use of a family of weighted Sobolev spaces, due to Kondrat'ev, for domains admitting corner singularities.
