Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows
In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error est...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Published: |
Society for Industrial and Applied Mathematics
2008
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/945/ |
| _version_ | 1848790508981190656 |
|---|---|
| author | Cliffe, Andrew Hall, Edward Houston, Paul |
| author_facet | Cliffe, Andrew Hall, Edward Houston, Paul |
| author_sort | Cliffe, Andrew |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. |
| first_indexed | 2025-11-14T18:13:44Z |
| format | Article |
| id | nottingham-945 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:13:44Z |
| publishDate | 2008 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-9452020-05-04T20:27:36Z https://eprints.nottingham.ac.uk/945/ Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows Cliffe, Andrew Hall, Edward Houston, Paul In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to eigenvalue/stability problems. The underlying analysis consists of constructing both a dual eigenvalue problem and a dual problem for the original base solution. In this way, errors stemming from both the numerical approximation of the original nonlinear flow problem, as well as the underlying linear eigenvalue problem are correctly controlled. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented. Society for Industrial and Applied Mathematics 2008 Article NonPeerReviewed Cliffe, Andrew, Hall, Edward and Houston, Paul (2008) Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows. SIAM Journal on Scientific Computing . ISSN 1064-8275 (Submitted) Incompressible flows hydrodynamic stability a posteriori error estimation adaptivity discontinuous Galerkin methods |
| spellingShingle | Incompressible flows hydrodynamic stability a posteriori error estimation adaptivity discontinuous Galerkin methods Cliffe, Andrew Hall, Edward Houston, Paul Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title | Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title_full | Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title_fullStr | Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title_full_unstemmed | Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title_short | Adaptive discontinuous Galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| title_sort | adaptive discontinuous galerkin methods for eigenvalue problems arising in incompressible fluid flows |
| topic | Incompressible flows hydrodynamic stability a posteriori error estimation adaptivity discontinuous Galerkin methods |
| url | https://eprints.nottingham.ac.uk/945/ |