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1、2DiscontinuousFiniteElementProceduresThediscontinuousfiniteelementmethodmakesuseofthesamefunctionspaceasthecontinuousmethod,butwithrelaxedcontinuityatinterelementboundaries.ItwasfirstintroducedbyReedandHill[1]forthesolutionoftheneutrontransportequation,anditshistoryandrecentdeve
2、lopmenthavebeenreviewedbyCockburnetal.[2,3].Theessentialideaofthemethodisderivedfromthefactthattheshapefunctionscanbechosensothateitherthefieldvariable,oritsderivativesorgenerallyboth,areconsidereddiscontinuousacrosstheelementboundaries,whilethecomputationaldomaincontinuityismai
3、ntained.Fromthispointofview,thediscontinuousfiniteelementmethodincludes,asitssubsets,boththefiniteelementmethodandthefinitedifference(orfinitevolume)method.Therefore,ithastheadvantagesofboththefinitedifferenceandthefiniteelementmethods,inthatitcanbeeffectivelyusedinconvection-do
4、minantapplications,whilemaintaininggeometricflexibilityandhigherlocalapproximationsthroughtheuseofhigherorderelements.Thisfeaturemakesituniquelyusefulforcomputationaldynamicsandheattransfer.Becauseofthelocalnatureofadiscontinuousformulation,noglobalmatrixneedstobeassembled;andth
5、us,thisreducesthedemandonthein-corememory.Theeffectsoftheboundaryconditionsontheinteriorfielddistributionsthengraduallypropagatethroughelement-by-elementconnection.Thisisanotherimportantfeaturethatmakesthismethodusefulforfluidflowcalculations.Computationalfluiddyanmicsisanevolvi
6、ngsubject,andveryrecentdevelopmentsintheareaarediscussedin[4].Intheliterature,thediscontinuousfiniteelementmethodisalsocalledthediscontinuousGalerkinmethod,orthediscontinuousGalerkinfiniteelementmethod,orthediscontinuousmethod[1,2,3,5,6].Thesetermswillbeusedinterchangeablythroug
7、houtthisbook.Thischapterintroducesthebasicideasofthediscontinuousfiniteelementmethodthroughsimpleandillustrativeexamples.Thekeywordhereisdiscontinuous.Variousviewshavebeenadaptedtointerprettheconceptofdiscontinuityandthreewidelyacceptedonesarepresentedbelow[5,7].Thediscontinuous
8、finiteelementformulationforboundaryvalueproblem
