A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations
We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which...
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| Format: | Article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2018
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| Online Access: | https://eprints.nottingham.ac.uk/55378/ |
| _version_ | 1848799154465144832 |
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| author | Allendes, Alejandro Otárola, Enrique Rankin, Richard |
| author_facet | Allendes, Alejandro Otárola, Enrique Rankin, Richard |
| author_sort | Allendes, Alejandro |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples. |
| first_indexed | 2025-11-14T20:31:09Z |
| format | Article |
| id | nottingham-55378 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:31:09Z |
| publishDate | 2018 |
| publisher | Society for Industrial and Applied Mathematics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-553782018-10-22T14:41:31Z https://eprints.nottingham.ac.uk/55378/ A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations Allendes, Alejandro Otárola, Enrique Rankin, Richard We derive globally reliable a posteriori error estimators for a linear-quadratic optimal control problem involving the generalized Oseen equations as state equations; control constraints are also considered. The corresponding local error indicators are locally efficient. The assumptions under which we perform the analysis are such that they can be satisfied for a wide variety of stabilized finite element methods as well as for standard finite element methods. When stabilized methods are considered, no a priori relation between the stabilization terms for the state and adjoint equations is required. If a lower bound for the inf-sup constant is available, a posteriori error estimators that are fully computable and provide guaranteed upper bounds on the norm of the error can be obtained. We illustrate the theory with numerical examples. Society for Industrial and Applied Mathematics 2018-07-12 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/55378/1/Generalized_Oseen.pdf Allendes, Alejandro, Otárola, Enrique and Rankin, Richard (2018) A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations. SIAM Journal on Scientific Computing, 40 (4). A2200-A2233. ISSN 1095-7197 linear–quadratic optimal control problems; generalized Oseen equations; Brinkman equations; Stokes equations; a posteriori error estimators; stabilized adaptive finite element methods http://dx.doi.org/10.1137/17M1139631 doi:10.1137/17M1139631 doi:10.1137/17M1139631 |
| spellingShingle | linear–quadratic optimal control problems; generalized Oseen equations; Brinkman equations; Stokes equations; a posteriori error estimators; stabilized adaptive finite element methods Allendes, Alejandro Otárola, Enrique Rankin, Richard A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title | A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title_full | A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title_fullStr | A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title_full_unstemmed | A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title_short | A posteriori error estimation for a PDE-constrained optimization problem involving the generalized Oseen equations |
| title_sort | posteriori error estimation for a pde-constrained optimization problem involving the generalized oseen equations |
| topic | linear–quadratic optimal control problems; generalized Oseen equations; Brinkman equations; Stokes equations; a posteriori error estimators; stabilized adaptive finite element methods |
| url | https://eprints.nottingham.ac.uk/55378/ https://eprints.nottingham.ac.uk/55378/ https://eprints.nottingham.ac.uk/55378/ |