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arXiv · 2008.00149

Hybridization and postprocessing in finite element exterior calculus

Gerard Awanou·Maurice Fabien·Johnny Guzmán·Ari Stern
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Abstract

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.

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Gerard Awanou, Maurice Fabien, Johnny Guzmán, Ari Stern. 2020-08-01. Hybridization and postprocessing in finite element exterior calculus. https://doi.org/10.1090/mcom/3743

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