Volume 27, Issue 6
A New Approach to Recovery of Discontinous Galerkin

Sebastian Franz, Lutz Tobiska & Helena Zarin

J. Comp. Math., 27 (2009), pp. 697-712.

Published online: 2009-12

Preview Full PDF 293 2015
Export citation
  • Abstract

A new recovery operator P : discQn (T) -> discQn+1(M) for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh T into a higher order polynomial space on a macro mesh M. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local L2-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.

  • Keywords

Discontinuous Galerkin Postprocessing Recovery

  • AMS Subject Headings

65N12 65N15 65N30.

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-27-697, author = {}, title = {A New Approach to Recovery of Discontinous Galerkin}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {6}, pages = {697--712}, abstract = {

A new recovery operator P : discQn (T) -> discQn+1(M) for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh T into a higher order polynomial space on a macro mesh M. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local L2-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.09-m2899}, url = {http://global-sci.org/intro/article_detail/jcm/8598.html} }
TY - JOUR T1 - A New Approach to Recovery of Discontinous Galerkin JO - Journal of Computational Mathematics VL - 6 SP - 697 EP - 712 PY - 2009 DA - 2009/12 SN - 27 DO - http://doi.org/10.4208/jcm.2009.09-m2899 UR - https://global-sci.org/intro/article_detail/jcm/8598.html KW - Discontinuous Galerkin KW - Postprocessing KW - Recovery AB -

A new recovery operator P : discQn (T) -> discQn+1(M) for discontinuous Galerkin is derived. It is based on the idea of projecting a discontinuous, piecewise polynomial solution on a given mesh T into a higher order polynomial space on a macro mesh M. In order to do so, we define local degrees of freedom using polynomial moments and provide global degrees of freedom on the macro mesh. We prove consistency with respect to the local L2-projection, stability results in several norms and optimal anisotropic error estimates. As an example, we apply this new recovery technique to a stabilized solution of a singularly perturbed convection-diffusion problem using bilinear elements.

Sebastian Franz, Lutz Tobiska & Helena Zarin. (2019). A New Approach to Recovery of Discontinous Galerkin. Journal of Computational Mathematics. 27 (6). 697-712. doi:10.4208/jcm.2009.09-m2899
Copy to clipboard
The citation has been copied to your clipboard