Anewalternatingdirection(AD)finiteelement(FE)schemefor3-dimensionalnonlinearparabolicequationandparabolicintegro-differentialequationisstudied.ByusingAD,the3-dimensionalproblemisreducedtoafamilyofsinglespacevariableproblems,calculationworkissimplified;byusingFE,highaccuracyiskept;byusingvarioustechniquesforprioriestimatefordifferentialequationssuchasinductivehypothesisreasoning,thedifficultyarisingfromthenonlinearityistreated.ForbothFEandADFEschemes,theconvergencepropertiesarerigorouslydemonstrated,theoptimalH1-andL2-normspaceestimatesandtheO((△t)2)estimatefortimevariableareobtained.
