OperationsResearchandFuzziology$ʆ��Æ,2023,13(4),4120-4131PublishedOnlineAugust2023inHans.https://www.hanspub.org/journal/orfhttps://doi.org/10.12677/orf.2023.134412äk˜mÿþêâ��Ô.•§.¡¯K�ŒlÑØ��O���ÊÊʧ§§ÛÛÛpppWWWB²ŒÆ§êƆÚOÆ�§B²B�ÂvFϵ2023c6�5F¶¹^Fϵ2023c8�15F¶uÙFϵ2023c8�23FÁ‡�©ïÄ�äk˜mÿÝêâ�‚5�Ô.¡¯K�k�Ø�©Û§éu˜m�lÑ·‚$^k•�lÑ��§�ŒlѯK§duÿÝ��K5�$§¤±¯K�)3�‡•Säké$��K5"|^L2ÝKŽfÚéó5ëê§3•��K5^‡e§�Ñ�˜mlÑk•�%C�L2‰ê¥�k�Ø��O"'…c˜mÿÝê⧌lѧL2‰ê§k�Ø��OSemi-DiscreteErrorEstimationoftheInterfaceProblemofParabolicEquationswithSpatialMeasurementDataXunYang,XianbingLuoSchoolofMathematicsandStatistics,GuizhouUniversity,GuiyangGuizhouReceived:Jun.5th,2023;accepted:Aug.15th,2023;published:Aug.23rd,2023©ÙÚ^:�Ê,ÛpW.äk˜mÿþêâ��Ô.•§.¡¯K�ŒlÑØ��O[J].$ʆ��Æ,2023,13(4):4120-4131.DOI:10.12677/orf.2023.134412�ʧÛpWAbstractInthispaper,westudytheapriorierroranalysisoflinearparabolicinterfaceprob-lemswithspatialmeasuredata.Forthespatialdiscretization,weusefiniteelementdiscretizationtoobtainitssemi-discreteproblem;becausethemeasureregularityislow,sothesolutionoftheproblemhasverylowregularityinthewholedomain.WederiveapriorerrorestimateintheL2normofthespatialdiscretefiniteelementapproximationunderminimumregularity,usingtheL2projectionoperatorandthedualityparameter.KeywordsSpatialMeasureData,Semi-Discrete,L2Norm,APrioriErrorEstimatesCopyrightc⃝2023byauthor(s)andHansPublishersInc.ThisworkislicensedundertheCreativeCommonsAttributionInternationalLicense(CCBY4.0).http://creativecommons.org/licenses/by/4.0/1.Úó�©ïÄ�äk˜mÿþêâ�‚5�Ô¡.¡¯K�˜mlÑk•�%C�k�Ø�©Û§=�������������ut−∇·(β∇u)=µ(x,t)∈ΩTu=0(x,t)∈ΓTu(·,0)=u0x∈Ω,(1.1)3ΓT1=Γ1×[0,T]þ÷ve¡�.¡a=^‡[u]=0,[β∂u∂n]=0.(1.2)Ù¥§Ω´R2¥�k.�àõ>/«•§ΩT=Ω×(0,T]§ΓT=Γ×(0,T]§ùp�>.Γ=∂Ω´|ÊF]>."...
