An extended Galerkin analysis in finite element exterior calculus
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- Math. Comp. 91 (2022), 1077-1106 Request permission
Abstract:
For the Hodge–Laplace equation in finite element exterior calculus, we introduce several families of discontinuous Galerkin methods in the extended Galerkin framework. For contractible domains, this framework utilizes seven fields and provides a unifying inf-sup analysis with respect to all discretization and penalty parameters. It is shown that the proposed methods can be hybridized as a reduced two-field formulation.References
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Additional Information
- Qingguo Hong
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 1007990
- Email: huq11@psu.edu
- Yuwen Li
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 1129421
- ORCID: 0000-0002-4071-8653
- Email: yuwenli925@gmail.com
- Jinchao Xu
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 228866
- Email: jxx1@psu.edu
- Received by editor(s): January 4, 2021
- Received by editor(s) in revised form: August 20, 2021, and October 16, 2021
- Published electronically: December 30, 2021
- Additional Notes: The third named author was supported by Center for Computational Mathematics and Applications, and the Verne M. William Professorship Fund from the Pennsylvania State University
The second named author is the corresponding author - © Copyright 2021 American Mathematical Society
- Journal: Math. Comp. 91 (2022), 1077-1106
- MSC (2020): Primary 65N12, 65N15, 65N30
- DOI: https://doi.org/10.1090/mcom/3707
- MathSciNet review: 4405489