%0 Generic %1 awanou2020hybridization %A Awanou, Gerard %A Fabien, Maurice %A Guzmán, Johnny %A Stern, Ari %D 2020 %K 58a14-Hodge-theory-in-global-analysis 65n30-pdes-bvps-finite-elements %T Hybridization and postprocessing in finite element exterior calculus %U http://arxiv.org/abs/2008.00149 %X We hybridize the methods of finite element exterior calculus for the Hodge-Laplace problem on differential $k$-forms in $R^n$. 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.

@misc{awanou2020hybridization, 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.}, added-at = {2020-10-21T03:47:47.000+0200}, author = {Awanou, Gerard and Fabien, Maurice and Guzmán, Johnny and Stern, Ari}, biburl = {https://www.bibsonomy.org/bibtex/264956ae6cfc4c539f6cf0a7d0004792e/gdmcbain}, howpublished = {arXiv.org > math > arXiv:2008.00149}, interhash = {70a8707a09e0545059a888c649990018}, intrahash = {64956ae6cfc4c539f6cf0a7d0004792e}, keywords = {58a14-Hodge-theory-in-global-analysis 65n30-pdes-bvps-finite-elements}, timestamp = {2020-10-21T03:47:47.000+0200}, title = {Hybridization and postprocessing in finite element exterior calculus}, url = {http://arxiv.org/abs/2008.00149}, year = 2020 }