Superconvergence for the gradient of finite element approximations by L2-projections

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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Bibliographic Details
Main Authors: Heimsund, Bjorn-Ove, Tai, Xue Cheng, Wang, Junping
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2009
Subjects:
DRNTU::Science::Mathematics::Applied mathematics::Numerical analysis
Online Access: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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Institution: Nanyang Technological University
Language: English
Description
Summary: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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