willbeinsertedbyhandlater NumerischeMathematikManuscript-Nr initialdata methodsforparabolicproblemswithnonsmooth Superconvergenceofmixed niteelement HongsenChen1 RichardEwing1 andRaytchoLazarov1 Inst...
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Abstract: initial-boundaryvalu eproblemsisintroduce dandanalyzed.Superco nvergence estimatesforbothpres sureandvelocityareob tained.Theestimatesf orthe smoothsolutions.Howe ver,forsmalltimeinte rvalsweobtainthecorr ectconerrorsinpressu reandvelocitydependo nthesmoothnessofthei nitialdatain-forlarg etimelevelsessential lycoincidewiththeest imatesobtainedearlie rfor vergenceordersfornon smoothdata. Becauseofthesmoothin gpropertiesofthepara bolicoperator,thesee stimates cludingthelimitingca sesofdatainL2anddata inHr,forrsucientlyla rge. MathematicsSubjectCl assication(1991):65M 30,65N30 1.Introduction Keywords:Parabolicpr oblem,mixedniteeleme ntmethod,superconver gence Sincethepioneeringwo rkofRaviartandThomas (Raviartetal.,1977), the drawntheattentionofm anyspecialistsinnume ricalpartialdierenti alequaasuxesorveloci tiesandleadstoscheme sthatarelocallyconse rvative.Howtions.Thi smethodprovidesdirec tapproximationofthep hysicalquantitiessuc h mixedniteelementappr oximationstosecond-o rderellipticproblems have physicalquantities(p ressureandvelocity,t emperatureandux,etc. )cannotbe
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