83_A posteriori error analysis and adaptive processes in the finite element method Part I—error analysis

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1、INTERNATIONALJOURNALFORNUMERICALMETHODSINENGINEERING,VOL.19,1593-1619(1983)APOSTERIORIERRORANALYSISANDADAPTIVEPROCESSESINTHEFINITEELEMENTMETHOD:PARTI-ERRORANALYSISD.W.KELLY,J.P.DES.R.GAG0AND0.C.ZIENKIEWICZDepartmentofCivilEngineering,UniversityCollegeofSwansea,U

2、.K.I.BABUSKAInstituteforPhysicalScienceandTechnology,UniversityofMaryland,U.S.A.SUMMARYThisisapaperpresentedintwopartsdealingrespectivelywitherroranalysisandadaptiveprocessesappliedtofiniteelementcalculations.PartIcontainsthebasictheoryandmethodsofderivingerrore

3、stimatesforsecond-orderproblems.PartI1ofthepaperdealswiththestrategyforadaptiverefinementandconcentratesonthep-convergentmethods.Itisshownthatanextremelyhighrateofconvergenceisreachedinpracticalproblemsusingsuchprocedures.Applicationstorealisticstressanalysisand

4、potentialproblemsarepresented.INTRODUCTIONThispaperisconcernedwiththeidentificationofthediscretizationerrorinthefiniteelementmethodandthedefinitionofoptimalrefinementprocesses.RecentlyBabuska,Rheinboldtandtheirco-workers'-'4havedevelopedaposteriorierrorestimates

5、forthebilinearelementwhicharesufficientlyrobusttoreliablyindicatewhentheerrorissmall.Closelyrelatedtothisworkhasbeenthedevelopmentofadaptiveschemeswhichautomaticallyenrichthefiniteelementmeshonthebasisoflocalerrorindicatorstogiveconvergencetonear-optimalmeshesan

6、dre-solveuntilaprespecifiedaccuracyisachieved.Thesemathematicalprocessesleadtothequestionofthelocalaswellasglobalinterpretationoftheerrorandthedefinitionofoptimalityinthefiniteelementmesh.Wewilladdressthesequestionsinthistwo-partpaper,aiminginthefirstparttosimpl

7、ifyandextendthederivationoftheerrorestimatorsandassesstheirreliability.InpartI1ofthepaper17wediscusstheadaptiveprocessesandthequestionofoptimalalgorithmstoachieveagivenaccuracy.Anattemptwillbemadetoidentifyboththestrengthsandweaknessesoftheapproacheswhicharecurr

8、entlyavailable,whethertheaimistoachieveaprocessforassessingtheerrorinagivensolutionorthedevelopmentoffullyautomatedproceduresinwhichtheaccuracyrequiredisprespecifiedi