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://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/894.html
KW - discontinuous Galerkin methods, a posteriori error estimation, adaptivity, compressible Navier-Stokes equations.
AB - <p style="text-align: justify;">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 a posteriori 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 meshes 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.</p>