简介：

简介：

简介：1.IntroductionTheaimofthisnoteistoestablishtheconvergenceofthenonconformingfiniteelementmethodsforthesecondorderellipticproblemwiththelowestregularity.Theproofoftheconvergenceisnottrivial,althoughtheconvergenceresultsfortheconformingfiniteelementmeth...

简介：Heattransportatthemicroscaleisofvitalimportanceinmicrotechnologyapplications.Theheattransportequationisdifferentfromthetraditionalheattransportequationsinceasecondorderderivativeoftemperaturewithrespecttotimeandathird-ordermixedderivativeoftemperaturewithrespecttospaceandtimeareintroduced.Inthisstudy,wedevelopahybridfiniteelement-finitedifference(FE-FD)schemewithtwolevelsintimeforthethreedimensionalheattransportequationinacylindricalthinfilmwithsubmicroscalethickness.Itisshownthattheschemeisunconditionallystable.Theschemeisthenemployedtoobtainthetemperatureriseinasub-microscalecylindricalgoldfilm.Themethodcanbeappliedtoobtainthetemperatureriseinanythinfilmswithsub-microscalethickness,wherethegeometryintheplanardirectionisarbitrary.