Analysis of Adjoint Error Correction for Superconvergent Functional Estimates
Earlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by usi...
| প্রধান লেখক: | , |
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| বিন্যাস: | Report |
| প্রকাশিত: |
Unspecified
2001
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| _version_ | 1826269470560092160 |
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| author | Giles, M Pierce, N |
| author_facet | Giles, M Pierce, N |
| author_sort | Giles, M |
| collection | OXFORD |
| description | Earlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by using an adjoint PDE solution to reveal the sensitivity of the functional to the residual error in the original PDE solution. The present work provides a priori error analysis that correctly predicts the behaviour of the remaining leading order error term. Furthermore, the discussion is extended from the case of homogeneous boundary conditions and bulk functionals, to encompass the possibilities of inhomogeneous boundary conditions and boundary functionals. Numerical illustrations are provided for both linear and nonlinear problems. This research was supported by EPSRC under grant GR/K91149, and by NASA/Ames Cooperative Agreement No. NCC 2-5431. |
| first_indexed | 2024-03-06T21:25:33Z |
| format | Report |
| id | oxford-uuid:42fa3324-3752-40ea-a823-d03f46f990ba |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:25:33Z |
| publishDate | 2001 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:42fa3324-3752-40ea-a823-d03f46f990ba2022-03-26T14:52:36ZAnalysis of Adjoint Error Correction for Superconvergent Functional EstimatesReporthttp://purl.org/coar/resource_type/c_93fcuuid:42fa3324-3752-40ea-a823-d03f46f990baMathematical Institute - ePrintsUnspecified2001Giles, MPierce, NEarlier work introduced the notion of adjoint error correction for obtaining superconvergent estimates of functional outputs from approximate PDE solutions. This idea is based on a posteriori error analysis suggesting that the leading order error term in the functional estimate can be removed by using an adjoint PDE solution to reveal the sensitivity of the functional to the residual error in the original PDE solution. The present work provides a priori error analysis that correctly predicts the behaviour of the remaining leading order error term. Furthermore, the discussion is extended from the case of homogeneous boundary conditions and bulk functionals, to encompass the possibilities of inhomogeneous boundary conditions and boundary functionals. Numerical illustrations are provided for both linear and nonlinear problems. This research was supported by EPSRC under grant GR/K91149, and by NASA/Ames Cooperative Agreement No. NCC 2-5431. |
| spellingShingle | Giles, M Pierce, N Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title | Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title_full | Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title_fullStr | Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title_full_unstemmed | Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title_short | Analysis of Adjoint Error Correction for Superconvergent Functional Estimates |
| title_sort | analysis of adjoint error correction for superconvergent functional estimates |
| work_keys_str_mv | AT gilesm analysisofadjointerrorcorrectionforsuperconvergentfunctionalestimates AT piercen analysisofadjointerrorcorrectionforsuperconvergentfunctionalestimates |