On Local Super-penalization of Interior Penalty Discontinuous Galerkin Methods

Volume 11, Issue 3

A. Cangiani, J. Chapman, E. Georgoulis & M. Jensen

Int. J. Numer. Anal. Mod., 11 (2014), pp. 478-495

Published online: 2014-11

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Abstract

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.

Keywords

discontinuous Galerkin methods finite elements interior penalty

AMS Subject Headings

65N30 65N55 65M60

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@Article{IJNAM-11-478, author = {A. Cangiani, J. Chapman, E. Georgoulis and M. Jensen}, title = {On Local Super-penalization of Interior Penalty Discontinuous Galerkin Methods}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {478--495}, abstract = {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.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/538.html} }

TY - JOUR T1 - On Local Super-penalization of Interior Penalty Discontinuous Galerkin Methods AU - A. Cangiani, J. Chapman, E. Georgoulis & M. Jensen JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 478 EP - 495 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/538.html KW - discontinuous Galerkin methods KW - finite elements KW - interior penalty AB - 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.

A. Cangiani, J. Chapman, E. Georgoulis & M. Jensen. (1970). On Local Super-penalization of Interior Penalty Discontinuous Galerkin Methods. International Journal of Numerical Analysis and Modeling. 11 (3). 478-495. doi:

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