论文标题
在有限元内表积分中的杂交和后处理
Hybridization and postprocessing in finite element exterior calculus
论文作者
论文摘要
我们将有限元元素外观计算的方法杂交在$ \ mathbb {r}^n $中的差异$ k $ - forms上的hodge-laplace问题。在$ k = 0 $和$ k = n $的情况下，我们恢复了标量泊松方程的众所周知的原始和混合混合方法，而对于$ 0 <k <n $，我们获得了新的混合有限元方法，包括$ n = 2 $和$ n = 3 $ dimensions $ n = 2 $中的矢量泊松方程的方法。我们还将Stenberg的后处理从$ k = n $概括为任意$ k $，证明了新的SuperConvergence估计。最后，我们讨论了如何将这种杂交框架扩展到包括不合格和杂交的不连续的Galerkin方法。
We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential $k$-forms in $\mathbb{R}^n$. In the cases $k = 0$ and $k = n$, we recover well-known primal and mixed hybrid methods for the scalar Poisson equation, while for $0 < k < n$, we obtain new hybrid finite element methods, including methods for the vector Poisson equation in $n = 2$ and $n = 3$ dimensions. We also generalize Stenberg postprocessing from $k = n$ to arbitrary $k$, proving new superconvergence estimates. Finally, we discuss how this hybridization framework may be extended to include nonconforming and hybridizable discontinuous Galerkin methods.
