热传导方程的新型间断有限元方法

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1、硕士学位论文热传导方程的新型间断有限元方法ANEWDISCONTINUOUSGALERKINMETHODFORHEATEQUATIONᵾ哈尔滨工业大学2015ᒤ7ᴸഭ޵മҖ࠶㊫ਧ˖O241.82学ṑԓ⸱˖10213ഭ䱵മҖ࠶㊫ਧ˖519.6ᇶ㓗˖ޜᔰ⨶学硕士学位论文热传导方程的新型间断有限元方法硕士研究生˖ᵾ导师˖ᕐ䗮⋫࢟ᮉᦸ申请学位˖⨶学硕士学科˖䇑㇇ᮠ学所在单位˖⨶学䲒ᮠ学㌫答辩日期˖2015ᒤ7ᴸ授予学位单位˖૸ቄ┘ᐕъབྷ学ClassifiedIndex:O241.82U.D.C:519.6Dissert

2、ationfortheMasterDegreeinScienceANEWDISCONTINUOUSGALERKINMETHODFORHEATEQUATIONCandidate:LiJiaSupervisor:Assoc.Prof.ZhangDazhiAcademicDegreeAppliedfor:MasterofScienceSpecialty:ComputationalMathematicsAffiliation:DepartmentofMathematicsDateofDefense:July,2015D

3、egree-Conferring-Institution:HarbinInstituteofTechnology૸ቄ┘ᐕъབྷ学⨶学硕士学位论文摘要ᵜ文⹄ウⲴѫ㾱޵ᇩѪᓄ⭘࣐ᵳᮠ٬⍱䙊䟿ᶴ䙐ᮠ٬Ṭᔿ⭘Ҿ≲䀓ਁኅᗞ࠶ᯩ〻ˈަѝᡰ⹄ウⲴਁኅᯩ〻Ѫ✝Րሬᯩ〻ˈ਼ᰦᵜ文ᓄ⭘䰤ᯝᴹ䲀٬ᮠ㹼䘋)MethodsGalerkinDiscontinuous(⌅ṬᔿⲴᶴ䙐DŽਁኅᯩ〻Ѫٿᗞ࠶ᯩ〻ѝа㊫ॱ࠶䟽㾱Ⲵᯩ〻ˈ൘、学⹄ウоᐕ〻ᓄ⭘ѝ䜭ᴹ⵰ᒯ⌋Ⲵᓄ⭘DŽᵜ文⹄ウⲴ✝Րሬᯩ〻ᱟਁኅᯩ〻ѝⲴа⿽ˈ኎Ҿᣋ⢙රٿᗞ࠶ᯩ〻ˈᱟ⭘ᶕ᧿䘠⢙⨶ѝ㔉

4、ᇊオ䰤४ฏ✝ᢙᮓᡆ㋂ᆀᢙᮓ⧠䊑Ⲵᮠ学⁑රDŽ䰤ᯝᴹ䲀ᯩ⌅ᴰᰙ㻛ᨀࠪҾ1973ᒤˈᱟа㊫⭘Ҿ≲䀓ٿᗞ࠶ᯩ〻Ⲵᮠ٬㇇⌅DŽᆳⲴṶᷦᶕⓀҾᴹ䲀⌅оᴹ䲀փ〟⌅ˈ䙊䗷᭩䘋ᡀѪа⿽ᴹ䖳儈㋮ᓖⲴᮠ٬ᯩ⌅ˈᒦф㜭ཏᓄ⭘Ҿ≲䀓Ὕശǃᣋ⢙оৼᴢරㅹ਴㊫ᯩ〻ˈ਼ᰦ൘਴亶ฏᴹᒯ⌋ൠᓄ⭘DŽ⭡Ҿ䰤ᯝᴹ䲀⌅ⲴสᵜṶᷦᶕ㠚ᴹ䲀⌅оᴹ䲀փ〟⌅ˈᡰԕᮠ٬⍱䙊䟿ᱟ䰤ᯝᴹ䲀ᯩ⌅ѝа亩ॱ࠶䟽㾱Ⲵ⹄ウ޵ᇩDŽᮠ٬⍱䙊䟿ᖰᖰߣᇊҶᮠ٬Ṭᔿᱟ੖㜭ཏሩٿᗞ࠶ᯩ〻䘋㹼≲䀓ԕ৺ᮠ٬ṬᔿⲴっᇊ઼᭦ᮋㅹᙗ䍘DŽ䖳ѪՐ㔏Ⲵᮠ٬⍱䙊䟿ᖒᔿᴹ䗾仾ᮠ٬⍱䙊䟿઼ѝᗳᮠ٬⍱䙊䟿ㅹˈᆳԜ㜭

5、ཏሩཊ⿽ᯩ〻䘋㹼≲䀓ᒦфᴹ䖳ྭⲴᙗ䍘DŽᵜ文ѝᡰ⭘Ⲵ࣐ᵳᮠ٬⍱䙊䟿˄䗾仾ᮠ٬⍱䙊䟿˅ᱟ⍱䙊䟿Ⲵа⿽ᖒᔿˈн਼Ҿ䗾仾઼ѝᗳᮠ٬⍱䙊䟿ˈᆳ䟷ਆঅ㢲⛩єחᮠ٬࣐ᵳⲴᖒᔿˈ㘼䶎ㆰঅൠਆঅ㢲⛩Ⲵঅחᮠ٬ᡆєחᮠ٬Ⲵᒣ൷ˈ䘉ᗇᆳ㜭ཏᓄሩ䖳Ѫ༽ᵲⲴᯩ〻ˈᒦфᴹ䖳ྭⲴ᭦ᮋᙗDŽഐ↔ˈ࣐ᵳᮠ٬⍱䙊䟿൘ḀӋᯩ䶒ާᴹՈҾަᆳ⍱䙊䟿Ⲵᙗ䍘DŽᵜ文ᓄ⭘࣐ᵳᮠ٬⍱䙊䟿ᶴ䙐Ҷ≲䀓✝Րሬᯩ〻Ⲵᯠර䰤ᯝᴹ䲀ᯩ⌅ᮠ٬Ṭᔿˈᒦфሩᮠ٬ṬᔿⲴっᇊᙗ࠶᷀о䈟ᐞՠ䇑䰞仈䘋㹼Ҷ⹄ウˈ਼ᰦ䙊䗷䇑㇇ᵪ㕆〻䘋㹼ᮠ٬ᇎ傼ˈᗇࡠⲴᮠ٬㔃᷌о䈟ᐞՠ䇑Ⲵ㔃论⴨ㅖਸˈ傼䇱Ҷᮠ٬

6、ṬᔿⲴᴹ᭸ᙗDŽ关键词：䰤ᯝᴹ䲀ᯩ⌅˗࣐ᵳᮠ٬⍱䙊䟿˗✝Րሬᯩ〻-I-૸ቄ┘ᐕъབྷ学⨶学硕士学位论文AbstractThisarticlestudiesthenumericalschemebyusingweightednumericalfluxforsolv-ingevolutionequation.Theevolutionequationthisarticlestudiesisheatequation,andthediscontinuousGalerkinmethodsisusedtodevelopthenum

7、ericalschemeforsolvingtheheatequation.Time-dependentequaitonisaclassofpartialdifferentialequation,whichplaysasignificantroleinscientificstudiesandengineeringapplications.Heatequation,amongmanykindsoftime-dependentequations,isatypeofparabolicequation,thatdesc

8、ribesthedistributionofheatorparticleinagivenregionovertime.DiscontinuousGalerkinmethods(DG)werefirstproposedandanalyzedin1973asanumericalmethodtosolvepartialdifferentialequation.DiscontinuousGal