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1、有限元分析离散方法（Finiteelementanalysisofdiscretemethods）Discretizationmethod:finitedifferencemethod,finiteelementmethod,finitevolumemethodTheso-calledregiondiscretization,Inessence,afinitesetofdiscretepointsisusedtoreplacetheoriginalcontinuousspace.Theimplementationprocessis;Dividethecalculatedareain
2、toanumberofnon-overlappingsub-regions,determinethenodelocationofeachsub-regionandthecontrolvolumerepresentedbythenode.Node:thegeometricalpositionofunknownphysicalquantitiesthatneedtobesolved;Controlvolume:minimumgeometricunitofappliedcontrolequationorconservationlaw.Anodeisgenerallyconsideredt
3、obearepresentativeofvolumecontrol.Thecontrolvolumeandsubregionsarenotalwayscoincident.Atthebeginningofthediscretizationprocess,thesmallregionofaseriesoflinesorcurvesthatcorrespondtotheaxesoftheaxesorcurvesiscalledsubregions.Gridisadiscretebasis,andgridnodesarethestoragelocationsofdiscretephysi
4、calquantities.Asyouknow,thecommonlyuseddiscretizationmethodsarefinitedifferencemethod,finiteelementmethod,finitevolumemethod.1.Finitedifferencemethodisthemostclassicalmethodinnumericalsolution.Itistosolvethedivisionfordifferencegrid,usingafinitenumberofgridnodesinsteadofcontinuoussolvingdomain
5、,thenthepartialdifferentialequation(controlequation)derivativedifferencequotientinsteadofcontainingthediscretepointofafinitenumberofunknownsisdeduceddifferentialequations.Thismethodhasbeendevelopedearlierandmoremature,whichisusedtosolvethehyperbolicandparabolicproblems.Usingittosolvethecomplic
6、atedboundaryconditions,especiallytheellipticalproblemislessconvenientthanfiniteelementmethodorfinitevolumemethod.2.Thefiniteelementmethod(fem)isacontinuousdomainarbitraryintoappropriateshapesofmanysmallunits,andconstructtheinterpolationfunctionineachsmallunitdivided,andthenaccordingtotheprinci
7、pleofextremum(variationalorweightedresidualmethod),theproblemofcontrolequationsintoallelementsonthefiniteelementequations,theoverallextremumextremumaseachunit,thesumofthelocalunittotalsynthesis,isembeddedinthespecifiedboundaryconditions
