Superconvergence for the gradient of finite element approximations by L2-projections
A gradient recovery technique is proposed and analyzed for finite element solutions which provides new gradient approximations with high order of accuracy. The recovery technique is based on the method of least-squares surface fitting in a finite-dimensional space corresponding to a coarse mesh. It...
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sg-ntu-dr.10356-907862023-02-28T19:37:11Z Superconvergence for the gradient of finite element approximations by L2-projections Heimsund, Bjorn-Ove Tai, Xue Cheng Wang, Junping School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis A gradient recovery technique is proposed and analyzed for finite element solutions which provides new gradient approximations with high order of accuracy. The recovery technique is based on the method of least-squares surface fitting in a finite-dimensional space corresponding to a coarse mesh. It is proved that the recovered gradient has a high order of superconvergence for appropriately chosen surface fitting spaces. The recovery technique is robust, efficient, and applicable to a wide class of problems such as the Stokes and elasticity equations. Published version 2009-08-12T02:15:02Z 2019-12-06T17:54:00Z 2009-08-12T02:15:02Z 2019-12-06T17:54:00Z 2002 2002 Journal Article Heimsund, B. O., Tai, X. C., & Wang, J. (2002). Superconvergence for the gradient of finite element approximations by L2-projections. SIAM Journal on Numerical Analysis, 40(4), 1263-1280. 0036-1429 https://hdl.handle.net/10356/90786 http://hdl.handle.net/10220/6049 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2002&volume=40&issue=4&spage=1263&epage=1280&aulast=Heimsund&aufirst=%20B%20%2DO&auinit=&title=SIAM%20Journal%20on%20Numerical%20Analysis&atitle=Superconvergence%20for%20the%20gradient%20of%20finite%20element%20approximations%20by%20L2%20projections&sici. 10.1137/S003614290037410X. en SIAM Journal on Numerical Analysis. SIAM Journal on Numerical Analysis © copyright 2002 Siam Society for Industrial and Applied Mathematics. The journal's website is located at http://www.siam.org/journals/sinum.php. 18 p. application/pdf |
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DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis Heimsund, Bjorn-Ove Tai, Xue Cheng Wang, Junping Superconvergence for the gradient of finite element approximations by L2-projections |
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A gradient recovery technique is proposed and analyzed for finite element solutions which provides new gradient approximations with high order of accuracy. The recovery technique is based on the method of least-squares surface fitting in a finite-dimensional space corresponding to a coarse mesh. It is proved that the recovered gradient has a high order of superconvergence for appropriately chosen surface fitting spaces. The recovery technique is robust, efficient, and applicable to a wide class of problems such as the Stokes and elasticity equations. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Heimsund, Bjorn-Ove Tai, Xue Cheng Wang, Junping |
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Article |
author |
Heimsund, Bjorn-Ove Tai, Xue Cheng Wang, Junping |
author_sort |
Heimsund, Bjorn-Ove |
title |
Superconvergence for the gradient of finite element approximations by L2-projections |
title_short |
Superconvergence for the gradient of finite element approximations by L2-projections |
title_full |
Superconvergence for the gradient of finite element approximations by L2-projections |
title_fullStr |
Superconvergence for the gradient of finite element approximations by L2-projections |
title_full_unstemmed |
Superconvergence for the gradient of finite element approximations by L2-projections |
title_sort |
superconvergence for the gradient of finite element approximations by l2-projections |
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2009 |
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https://hdl.handle.net/10356/90786 http://hdl.handle.net/10220/6049 http://sfxna09.hosted.exlibrisgroup.com:3410/ntu/sfxlcl3?sid=metalib:ELSEVIER_SCOPUS&id=doi:&genre=&isbn=&issn=&date=2002&volume=40&issue=4&spage=1263&epage=1280&aulast=Heimsund&aufirst=%20B%20%2DO&auinit=&title=SIAM%20Journal%20on%20Numerical%20Analysis&atitle=Superconvergence%20for%20the%20gradient%20of%20finite%20element%20approximations%20by%20L2%20projections&sici. |
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