Volume 3, Issue 2
Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-oriented a Posteriori Error Estimation

R. Hartmann & P. Houston

DOI:

Int. J. Numer. Anal. Mod., 3 (2006), pp. 141-162

Published online: 2006-03

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  • Abstract

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier-Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I aposteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element me shes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.

  • Keywords

discontinuous Galerkin methods a posteriori error estimation adaptivity compressible Navier-Stokes equations

  • AMS Subject Headings

65N15 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-141, author = {R. Hartmann and P. Houston}, title = {Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-oriented a Posteriori Error Estimation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {2}, pages = {141--162}, abstract = {In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier-Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I aposteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element me shes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/894.html} }
TY - JOUR T1 - Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-oriented a Posteriori Error Estimation AU - R. Hartmann & P. Houston JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 141 EP - 162 PY - 2006 DA - 2006/03 SN - 3 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/894.html KW - discontinuous Galerkin methods KW - a posteriori error estimation KW - adaptivity KW - compressible Navier-Stokes equations AB - In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier-Stokes equations. In particular, we consider the a posteriori error analysis and adaptive mesh design for the underlying discretization method. Indeed, by employing a duality argument (weighted) Type I aposteriori bounds are derived for the estimation of the error measured in terms of general target functionals of the solution; these error estimates involve the product of the finite element residuals with local weighting terms involving the solution of a certain dual problem that must be numerically approximated. This general approach leads to the design of economical finite element me shes specifically tailored to the computation of the target functional of interest, as well as providing efficient error estimation. Numerical experiments demonstrating the performance of the proposed approach will be presented.
R. Hartmann & P. Houston. (1970). Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal-oriented a Posteriori Error Estimation. International Journal of Numerical Analysis and Modeling. 3 (2). 141-162. doi:
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