A Modified Polynomial Preserving Recovery and Its Applications to A Posteriori Error Estimates

(整期优先)网络出版时间:2010-01-11
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Amodifiedpolynomialpreservinggradientrecoverytechniqueisproposed.Unlikethepolynomialpreservinggradientrecoverytechnique,thegradientrecoveredwiththemodifiedpolynomialpreservingrecovery(MPPR)isconstructedelement-wise,anditisdiscontinuousacrosstheinterioredges.OneadvantageoftheMPPRtechniqueisthattheimplementationiseasierwhenadaptivemeshesareinvolved.SuperconvergenceresultsofthegradientrecoveredwithMPPRareprovedforfiniteelementmethodsforellipticboundaryproblemsandeigenvalueproblemsunderadaptivemeshes.TheMPPRisappliedtoadaptivefiniteelementmethodstoconstructasymptoticexactaposteriorierrorestimates.Numericaltestsareprovidedtoexaminethetheoreticalresultsandtheeffectivenessoftheadaptivefiniteelementalgorithms.