Skip to Main content Skip to Navigation
Theses

Discountinuous Galerkin methods and posteriori error analysis for heterogeneous diffusion problems

Abstract : In this thesis we analyse a discontinuous Galerkin (DG) method and two computable a posteriori error estimators for the linear and stationary advection-diffusion-reaction equation with heterogeneous diffusion. The DG method considered, the SWIP method, is a variation of the Symmetric Interior Penalty Galerkin method. The difference is that the SWIP method uses weighted averages with weights that depend on the diffusion. The a priori analysis shows optimal convergence with respect to mesh-size and robustness with respect to heterogeneous diffusion, which is confirmed by numerical tests. Both a posteriori error estimators are of the residual type and control the energy (semi-)norm of the error. Locallower bounds are obtained showing that almost all indicators are independent of heterogeneities. The exception is for the non-conforming part of the error, which has been evaluated using the Oswald interpolator. The second error estimator is sharper in its estimate with respect to the first one, but it is slightly more costly. This estimator is based on the construction of an H(div)-conforming Raviart-Thomas-Nédéléc flux using the conservativity of DG methods. Numerical results show that both estimators can be used for mesh-adaptation.
Document type :
Theses
Complete list of metadatas

https://pastel.archives-ouvertes.fr/pastel-00003419
Contributor : Ecole Des Ponts Paristech <>
Submitted on : Friday, February 22, 2008 - 8:00:00 AM
Last modification on : Friday, February 22, 2008 - 8:00:00 AM
Long-term archiving on: : Wednesday, September 8, 2010 - 5:57:33 PM

Identifiers

  • HAL Id : pastel-00003419, version 1

Collections

Citation

Annette Fagerhaug Stephansen. Discountinuous Galerkin methods and posteriori error analysis for heterogeneous diffusion problems. Engineering Sciences [physics]. Ecole des Ponts ParisTech, 2007. English. ⟨pastel-00003419⟩

Share

Metrics

Record views

380

Files downloads

233