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: | Article |
| Language: | en_US |
| Published: |
2003
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| Online Access: | http://hdl.handle.net/1721.1/3698 |
| _version_ | 1826210321245667328 |
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| author | Sauer-Budge, A.M. Huerta, A. Bonet, J. Peraire, Jaime |
| author_facet | Sauer-Budge, A.M. Huerta, A. Bonet, J. Peraire, Jaime |
| 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 | 2024-09-23T14:47:59Z |
| format | Article |
| id | mit-1721.1/3698 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:47:59Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | mit-1721.1/36982019-04-12T08:09:10Z Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation Sauer-Budge, A.M. Huerta, A. Bonet, J. Peraire, Jaime finite element output bounds a posteriori error estimation Poisson 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 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. Singapore-MIT Alliance (SMA) 2003-11-17T17:21:07Z 2003-11-17T17:21:07Z 2003-01 Article http://hdl.handle.net/1721.1/3698 en_US High Performance Computation for Engineered Systems (HPCES); 229367 bytes application/pdf application/pdf |
| spellingShingle | finite element output bounds a posteriori error estimation Poisson equation Sauer-Budge, A.M. Huerta, A. Bonet, J. Peraire, Jaime 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 | finite element output bounds a posteriori error estimation Poisson equation |
| url | http://hdl.handle.net/1721.1/3698 |
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