Adjoint recovery of superconvergent functionals from PDE approximations
Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an ad...
| Asıl Yazarlar: | , |
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| Materyal Türü: | Journal article |
| Baskı/Yayın Bilgisi: |
SIAM
2000
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| _version_ | 1826264536218337280 |
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| author | Pierce, N Giles, M |
| author_facet | Pierce, N Giles, M |
| author_sort | Pierce, N |
| collection | OXFORD |
| description | Motivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasi-one-dimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. |
| first_indexed | 2024-03-06T20:09:23Z |
| format | Journal article |
| id | oxford-uuid:2a0dda3c-7c48-4715-93f8-338c11a5ae19 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:09:23Z |
| publishDate | 2000 |
| publisher | SIAM |
| record_format | dspace |
| spelling | oxford-uuid:2a0dda3c-7c48-4715-93f8-338c11a5ae192022-03-26T12:22:43ZAdjoint recovery of superconvergent functionals from PDE approximationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2a0dda3c-7c48-4715-93f8-338c11a5ae19Mathematical Institute - ePrintsSIAM2000Pierce, NGiles, MMotivated by applications in computational fluid dynamics, a method is presented for obtaining estimates of integral functionals, such as lift or drag, that have twice the order of accuracy of the computed flow solution on which they are based. This is achieved through error analysis that uses an adjoint PDE to relate the local errors in approximating the flow solution to the corresponding global errors in the functional of interest. Numerical evaluation of the local residual error together with an approximate solution to the adjoint equations may thus be combined to produce a correction for the computed functional value that yields the desired improvement in accuracy. Numerical results are presented for the Poisson equation in one and two dimensions and for the nonlinear quasi-one-dimensional Euler equations. The theory is equally applicable to nonlinear equations in complex multidimensional domains and holds great promise for use in a range of engineering disciplines in which a few integral quantities are a key output of numerical approximations. |
| spellingShingle | Pierce, N Giles, M Adjoint recovery of superconvergent functionals from PDE approximations |
| title | Adjoint recovery of superconvergent functionals from PDE approximations |
| title_full | Adjoint recovery of superconvergent functionals from PDE approximations |
| title_fullStr | Adjoint recovery of superconvergent functionals from PDE approximations |
| title_full_unstemmed | Adjoint recovery of superconvergent functionals from PDE approximations |
| title_short | Adjoint recovery of superconvergent functionals from PDE approximations |
| title_sort | adjoint recovery of superconvergent functionals from pde approximations |
| work_keys_str_mv | AT piercen adjointrecoveryofsuperconvergentfunctionalsfrompdeapproximations AT gilesm adjointrecoveryofsuperconvergentfunctionalsfrompdeapproximations |