Approximation of Parametric Derivatives by the Empirical Interpolation Method
We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approx...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2013
|
| Online Access: | http://hdl.handle.net/1721.1/80806 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826212806121226240 |
|---|---|
| author | Grepl, Martin A. Patera, Anthony T. Ronquist, Einar M. Eftang, Jens L. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Grepl, Martin A. Patera, Anthony T. Ronquist, Einar M. Eftang, Jens L. |
| author_sort | Grepl, Martin A. |
| collection | MIT |
| description | We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory. |
| first_indexed | 2024-09-23T15:38:29Z |
| format | Article |
| id | mit-1721.1/80806 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:38:29Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/808062022-10-02T03:04:34Z Approximation of Parametric Derivatives by the Empirical Interpolation Method Grepl, Martin A. Patera, Anthony T. Ronquist, Einar M. Eftang, Jens L. Massachusetts Institute of Technology. Department of Mechanical Engineering Eftang, Jens L. Patera, Anthony T. We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory. 2013-09-19T14:10:19Z 2013-09-19T14:10:19Z 2012-06 2011-09 Article http://purl.org/eprint/type/JournalArticle 1615-3375 1615-3383 http://hdl.handle.net/1721.1/80806 Eftang, Jens L., Martin A. Grepl, Anthony T. Patera, and Einar M. Rønquist. Approximation of Parametric Derivatives by the Empirical Interpolation Method. Foundations of Computational Mathematics (June 19, 2012). https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1007/s10208-012-9125-9 Foundations of Computational Mathematics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag MIT web domain |
| spellingShingle | Grepl, Martin A. Patera, Anthony T. Ronquist, Einar M. Eftang, Jens L. Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title | Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title_full | Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title_fullStr | Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title_full_unstemmed | Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title_short | Approximation of Parametric Derivatives by the Empirical Interpolation Method |
| title_sort | approximation of parametric derivatives by the empirical interpolation method |
| url | http://hdl.handle.net/1721.1/80806 https://orcid.org/0000-0002-2631-6463 |
| work_keys_str_mv | AT greplmartina approximationofparametricderivativesbytheempiricalinterpolationmethod AT pateraanthonyt approximationofparametricderivativesbytheempiricalinterpolationmethod AT ronquisteinarm approximationofparametricderivativesbytheempiricalinterpolationmethod AT eftangjensl approximationofparametricderivativesbytheempiricalinterpolationmethod |