论文标题
Hodge Laplace问题的原始有限元方案
A primal finite element scheme of the Hodge Laplace problem
论文作者
论文摘要
In this paper, a unified family, for any $n\geqslant 2$ and $1\leqslant k\leqslant n-1$, of nonconforming finite element schemes are presented for the primal weak formulation of the $n$-dimensional Hodge-Laplace equation on $HΛ^k\cap H^*_0Λ^k$ and on the simplicial subdivisions of the domain.有限元方案具有足够常规数据的$ \ MATHCAL {O}（H）$ - 订单收敛率，而$ \ Mathcal {O}（H^S）$ - 任何$ S $ regular domain的订单率，$ 0 <s \ s \ s \ s \ leqslant 1 $，无论何种拓扑都没有拓扑。
In this paper, a unified family, for any $n\geqslant 2$ and $1\leqslant k\leqslant n-1$, of nonconforming finite element schemes are presented for the primal weak formulation of the $n$-dimensional Hodge-Laplace equation on $HΛ^k\cap H^*_0Λ^k$ and on the simplicial subdivisions of the domain. The finite element scheme possesses an $\mathcal{O}(h)$-order convergence rate for sufficiently regular data, and an $\mathcal{O}(h^s)$-order rate on any $s$-regular domain, $0<s\leqslant 1$, no matter what topology the domain has.
