Computation of accurate nodal derivatives of finite element solutions : The finite node displacement method

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DOIResolve DOI: http://doi.org/10.1002/nme.1979
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TypeArticle
Journal titleInternational Journal for Numerical Methods in Engineering
Volume71
Issue10
Pages11811207; # of pages: 28
SubjectFinite elements; nodal derivatives; node displacement; error estimation; boundary derivatives
AbstractThis paper presents a new method for extracting high accuracy nodal derivatives from finite element solutions. The approach involves imposing a finite displacement to individual mesh nodes, and solving a very small problem on the patch of surrounding elements, whose only unknown is the value of the solution at the displaced node. A finite difference between the original and perturbed values provides the directional derivative. Verification is shown for a 1D diffusion problem with exact nodal solution and for 2D scalar advective-diffusive problems. For internal nodes the method yields accuracy slightly superior to that of the superconvergent patch recovery technique of Zienkiewicz and Zhu (ZZ). We also present a variant of the method to treat boundary nodes. In this case the local discretization is enriched by inserting an additional mesh point very close to the boundary node of interest. We show that the new method gives normal derivatives at boundary points that are consistent with the so-called 'auxiliary fluxes'. The resulting nodal derivatives are much more accurate than those obtained by the ZZ superconvergent patch recovery technique.
Publication date
LanguageEnglish
AffiliationNational Research Council Canada (NRC-CNRC); NRC Industrial Materials Institute
Peer reviewedYes
NRC number48972
NPARC number15775002
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Record identifier6eba371d-602e-4a90-9192-2a5848a7071c
Record created2010-07-06
Record modified2016-05-09
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