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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2008.00149 |
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| _version_ | 1866916766623465472 |
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| author | Awanou, Gerard Fabien, Maurice Guzmán, Johnny Stern, Ari |
| author_facet | Awanou, Gerard Fabien, Maurice Guzmán, Johnny Stern, Ari |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_00149 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hybridization and postprocessing in finite element exterior calculus Awanou, Gerard Fabien, Maurice Guzmán, Johnny Stern, Ari Numerical Analysis 65N30 (Primary) 58A14 (Secondary) 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. |
| title | Hybridization and postprocessing in finite element exterior calculus |
| topic | Numerical Analysis 65N30 (Primary) 58A14 (Secondary) |
| url | https://arxiv.org/abs/2008.00149 |