Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems
We introduce a discontinuous finite volume method for the approximation of distributed optimal control problems governed by the Brinkman equations, where a force field is sought such that it produces a desired velocity profile. The discretisation of state and co-state variables follows a lowest-orde...
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| Format: | Journal article |
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Springer Verlag
2018
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| _version_ | 1826257490622283776 |
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| author | Kumar, S Ruiz Baier, R Sandilya, R |
| author_facet | Kumar, S Ruiz Baier, R Sandilya, R |
| author_sort | Kumar, S |
| collection | OXFORD |
| description | We introduce a discontinuous finite volume method for the approximation of distributed optimal control problems governed by the Brinkman equations, where a force field is sought such that it produces a desired velocity profile. The discretisation of state and co-state variables follows a lowest-order scheme, whereas three different approaches are used for the control representation: a variational discretisation, and approximation through piecewise constant and piecewise linear elements. We employ the optimise-then-discretise approach, resulting in a non-symmetric discrete formulation. A priori error estimates for velocity, pressure, and control in natural norms are derived, and a set of numerical examples is presented to illustrate the performance of the method and to confirm the predicted accuracy of the generated approximations under various scenarios. |
| first_indexed | 2024-03-06T18:19:03Z |
| format | Journal article |
| id | oxford-uuid:05a2fc9a-ec43-40c0-a98d-ce00f322b41f |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:19:03Z |
| publishDate | 2018 |
| publisher | Springer Verlag |
| record_format | dspace |
| spelling | oxford-uuid:05a2fc9a-ec43-40c0-a98d-ce00f322b41f2022-03-26T08:58:17ZError bounds for discontinuous finite volume discretisations of Brinkman optimal control problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:05a2fc9a-ec43-40c0-a98d-ce00f322b41fSymplectic Elements at OxfordSpringer Verlag2018Kumar, SRuiz Baier, RSandilya, RWe introduce a discontinuous finite volume method for the approximation of distributed optimal control problems governed by the Brinkman equations, where a force field is sought such that it produces a desired velocity profile. The discretisation of state and co-state variables follows a lowest-order scheme, whereas three different approaches are used for the control representation: a variational discretisation, and approximation through piecewise constant and piecewise linear elements. We employ the optimise-then-discretise approach, resulting in a non-symmetric discrete formulation. A priori error estimates for velocity, pressure, and control in natural norms are derived, and a set of numerical examples is presented to illustrate the performance of the method and to confirm the predicted accuracy of the generated approximations under various scenarios. |
| spellingShingle | Kumar, S Ruiz Baier, R Sandilya, R Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title | Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title_full | Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title_fullStr | Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title_full_unstemmed | Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title_short | Error bounds for discontinuous finite volume discretisations of Brinkman optimal control problems |
| title_sort | error bounds for discontinuous finite volume discretisations of brinkman optimal control problems |
| work_keys_str_mv | AT kumars errorboundsfordiscontinuousfinitevolumediscretisationsofbrinkmanoptimalcontrolproblems AT ruizbaierr errorboundsfordiscontinuousfinitevolumediscretisationsofbrinkmanoptimalcontrolproblems AT sandilyar errorboundsfordiscontinuousfinitevolumediscretisationsofbrinkmanoptimalcontrolproblems |