Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension

Volume 11, Issue 3

G. Csorgo & F. Izsak

Int. J. Numer. Anal. Mod., 11 (2014), pp. 567-586

Published online: 2014-11

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Abstract

Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an error estimation is obtained in the H¹-seminorm. We point out that this average can be regarded as a lower order modification of the average of a well-known overpenalized symmetric interior penalty (IP) method. This allows a natural derivation of the overpenalized IP methods.

Keywords

discontinuous Galerkin method smoothing technique and error estimation

AMS Subject Headings

65N12 65N15 65N30

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@Article{IJNAM-11-567, author = {G. Csorgo and F. Izsak}, title = {Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {567--586}, abstract = {Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an error estimation is obtained in the H¹-seminorm. We point out that this average can be regarded as a lower order modification of the average of a well-known overpenalized symmetric interior penalty (IP) method. This allows a natural derivation of the overpenalized IP methods.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/542.html} }

TY - JOUR T1 - Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension AU - G. Csorgo & F. Izsak JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 567 EP - 586 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/542.html KW - discontinuous Galerkin method KW - smoothing technique KW - and error estimation AB - Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an error estimation is obtained in the H¹-seminorm. We point out that this average can be regarded as a lower order modification of the average of a well-known overpenalized symmetric interior penalty (IP) method. This allows a natural derivation of the overpenalized IP methods.

G. Csorgo & F. Izsak. (1970). Energy Norm Error Estimates for Averaged Discontinuous Galerkin Methods in 1 Dimension. International Journal of Numerical Analysis and Modeling. 11 (3). 567-586. doi:

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