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Interior Penalty Continuous and Discontinuous Finite Element Approximations of Hyperbolic Equations
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posted on 2023-06-08, 10:08 authored by Erik Burman, Alfio Quarteroni, Benjamin StammIn this paper we present in a unified setting the continuous and discontinuous Galerkin methods for the numerical approximation of the scalar hyperbolic equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient across element faces in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and optionally of its gradient is required to achieve optimal convergence. We prove that the solution in the case of the continuous Galerkin approach can be considered as a limit of the discontinuous one when the stabilization parameter associated with the penalization of the solution jump tends to infinity. As a consequence, the limit of the numerical flux of the discontinuous method yields a numerical flux for the continuous method as well. Numerical results will highlight the theoretical results that are proven in this paper.
History
Publication status
- Published
ISSN
0885-7474Publisher
SPRINGER/PLENUM PUBLISHERS, 233 SPRING ST, NEW YORK, NY 10013 USAExternal DOI
Issue
3Volume
43Page range
293-312Presentation Type
- paper
Event name
International Conference on Recent Developments of Numerical Schemes for Flow ProblemsEvent location
Fukuoka, JAPAN, JUN 27-29, 2007Event type
conferenceDepartment affiliated with
- Mathematics Publications
Notes
SOURCE: JOURNAL OF SCIENTIFIC COMPUTINGFull text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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