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On local super-penalization of interior penalty discontinuous Galerkin methods

journal contribution
posted on 2023-06-08, 17:29 authored by Andrea Cangiani, John Chapman, Emmanuil Georgoulis, Max Jensen
We prove in an abstract setting that standard (continuous) Galerkin finite element approximations are the limit of interior penalty discontinuous Galerkin approximations as the penalty parameter tends to infinity. We apply this result to equations of non-negative characteristic form and the non-linear, time dependent system of incompressible miscible displacement. Moreover, we investigate varying the penalty parameter on only a subset of a triangulation and the effects of local super-penalization on the stability of the method, resulting in a partly continuous, partly discontinuous method in the limit. An iterative automatic procedure is also proposed for the determination of the continuous region of the domain without loss of stability of the method.

History

Publication status

  • Published

Journal

International Journal of Numerical Analysis & Modeling

ISSN

1705-5105

Publisher

University of Alberta

Issue

3

Volume

11

Page range

478-495

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2014-06-02

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