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1、INTERNATIONALJOURNAL,FORNUMERICALMETHODSINENGINEERING,VOL.19,1621-1656APOSTERIORIERRORANALYSISANDADAPTIVEPROCESSESINTHEFINITEELEMENTMETHOD:PART11-ADAPTIVEMESHREFINEMENTJ.P.DES.R.GAGO,D.W.KELLYAND0.C.ZIENKIEWICZDepartmentofCivilEngineering,UniversityColl
2、egeofSwansea,U.K.I.BABUSKAInstituteforPhysicalScienceandTechnology,UniversityofMaryland,U.S.A.SUMMARYThisisapaperpresentedintwopartsdealingrespectivelywitherroranalysisandadaptiveprocessesappliedtofiniteelementcalculations.PartIcontainsthebasictheoryand
3、methodsofderivingerrorestimatesforsecond-orderproblems.PartI1ofthepaperdealswiththestrategyforadaptiverefinementandconcentratesagainonthep-convergentmethods.Itisshownthatanextremelyhighrateofconvergenceisreachedinpracticalproblemsusingsuchprocedures.App
4、licationstorealisticstressanalysisandpotentialproblemsarepresented.INTRODUCTIONTheanalysisdescribedinPartIofthispaperhadasitsobjectivetheestimationoftheerrorinagivenfiniteelementsolutionandtheidentificationoftheregionsforrefinementgiventhatthepresentsol
5、utionisinsomewaydeficient.Forthispurposetheconceptoferrorestimatorsandindicatorswasdeveloped,theestimatorsgivingarelativelyaccuratemeasureoftheerrorinagivenmeshandtheindicatorsameasureofthechangeinenergyassociatedwiththeintroductionofanewvariable.Inthis
6、secondpartofthepaperweshallbeconcernedwiththeimportantengineeringproblemofachievingasolutionofagivenaccuracywiththeminimumtotalcost.Muchefforthasbeenputinthedeterminationofoptimalmeshesinthesensethattheerrorwasminimizedforagivennumberofdegrees-of-freedo
7、m(seeMcNeiceandMar~al,~~andFelippa31.”).Withthecostofthisoptimizationbeingprohibitive,generalguidelines,frequentlyusedinpractice,wereestablishedtoobtainefficientmeshes(seeOliveira,slT~rcke,~~,~~Meloshetal.44-46andShephardet~l.~~,~’).However,thebasicprob
8、lemofachievingaspecificaccuracycannotbesoaddressedandweproposeadifferentpath.Westartfromanarbitrarilydefinedmesh,usingifavailableanypreviousexperienceinsolvingsimilarproblems,andthenestimatetheerrorinthesolution.Ifthiserrorestima
