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1、ANEWVIEWPOINTONMIXEDELEMENTS*A.BOSSAVITEDF-ElectricitddeFrance,DirectiondesEtudesetRecherches,IAv.duGPntraldeGaulle,92141Clamart,France(Received:30May1991;acceptedinrevisedform:30July1991)ABSTRACT.Mixedelementsarespecialfiniteelementsforvectorfields,whoseshapefunctionsarenotnecessarilyco
2、ntinuousinalltheircomponents.Theyareusedinconnectionwith‘two-field’formulations,forinstancewhenonetriessimultaneouslytocomputedisplacementandstressmelasticity.Wepresenthereafamilyoffiniteelementswhichoriginatefromachapterofdifferentialgeometryapparentlyunconnectedwithnumericalanalysis(Wh
3、itneyforms)andinsistonthestructuralpropertiesofthisfamilyconsideredasawhole.Thisshedsanewlightonmixedelements,underwhichtheyacquireamorenaturalcharacterthaninpreviouspresentations.SOMMARIO.Glielementimistisonoelementifinitispecial1percampivettorialilecuifunzionidiinterpolazionenonsononec
4、essariamentecontinueintuttelecomponenti;talielementivengonousatinell’ambitodelleformulazioni‘aduecampi’,peresempioquandosicalcolanosimultaneamentespostamentoetensioneinelasticita.Inquest0articolovienepresentataunafamigliadielementilinitithetraggonooriginedauncostruttodigeometriadifferenz
5、ialetheinapparenzanonhaalcunnessoconl’analisinumerica(leformediWhitney):vengonoillustrateleproprietastrutturalicomplessivedttalefamiglia.Questapresentazionegettaunanuovalutesuglielementimisti,sottolaqualeessiacquistanouncaratterepiunaturale.KEYWORDS:EllipticPDEs,Finiteelements,Mixedeleme
6、nts,Differentialgeometry,Whitneyforms,Tontidiagrams,Complementarity,DualityThispaperisanattempttomergetwocurrentmodesofpurpose;theylacksomepropertyofconsistency,bestthoughtinnumericalanalysiswhich,inourview,haveexpressedbythefamous‘Ladyzhenskaya-Babuska-beenimportantduringthelast15years.
7、OneismixedBrezzi(LBB)condition’[2,9].Indeed,onemaytodayelements,awidelyknowntopic;theotherisTontidiagrams,understandtheeffortsdoneduringtheseventiesinthelesspopular,butunjustlyso.directionofmixedelements,asattemptstobuildconsist-Mixedelementsarespecialfiniteelements,‘non-
