Inthispaper,finitevolumemethodonunstructuredmeshesisstudiedforaparabolicconvection-diffusionproblemonanopenboundedsetofR^d(d=2or3)withRobinboundarycondition.UpwindingapproximationsareadaptedtotreatboththeconvectiontermandRobinboundarycondition.Bydirectlygettingstartfromtheformulationofthefinitevolumescheme,numericalanalysisisdone.Byusingseveraldiscretefunctionalanalysistechniquessuchassummationbyparts,discretenorminequality,etal,thestabilityanderrorestimatesontheapproximatesolutionareestablished,existenceanduniquenessoftheapproximatesolutionandthe1stordertemporalnormandL^2andH^1spacialnormconvergencepropertiesareobtained.
