Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation
We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level...
| Main Authors: | , , , |
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| Format: | Technical Report |
| Language: | en_US |
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Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/57596 |
| _version_ | 1826212820794998784 |
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| author | Sauer-Budge, A. M. Bonet, J. Huerta, A. Peraire, J. |
| author_facet | Sauer-Budge, A. M. Bonet, J. Huerta, A. Peraire, J. |
| author_sort | Sauer-Budge, A. M. |
| collection | MIT |
| description | We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization. |
| first_indexed | 2024-09-23T15:38:27Z |
| format | Technical Report |
| id | mit-1721.1/57596 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:38:27Z |
| publishDate | 2010 |
| publisher | Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/575962019-04-13T00:05:22Z Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation Sauer-Budge, A. M. Bonet, J. Huerta, A. Peraire, J. Poisson Equation A Posteriori Error Estimation Output Bounds Finite Element We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization. 2010-08-27T19:36:50Z 2010-08-27T19:36:50Z 2003 Technical Report http://hdl.handle.net/1721.1/57596 en_US ACDL Technical Reports;FDRL TR-03-1 application/pdf Aerospace Computational Design Laboratory, Dept. of Aeronautics & Astronautics, Massachusetts Institute of Technology |
| spellingShingle | Poisson Equation A Posteriori Error Estimation Output Bounds Finite Element Sauer-Budge, A. M. Bonet, J. Huerta, A. Peraire, J. Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title | Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title_full | Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title_fullStr | Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title_full_unstemmed | Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title_short | Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation |
| title_sort | computing bounds for linear functionals of exact weak solutions to poisson s equation |
| topic | Poisson Equation A Posteriori Error Estimation Output Bounds Finite Element |
| url | http://hdl.handle.net/1721.1/57596 |
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