AD(Alternatingdirection)Galerkinschemesford-dimensionalnonlinearpseudo-hyperbolicequationsarestudied.Byusingpatchapproximationtechnique,ADprocedureisrealized,andcalculation,workissimplified.ByusingGalerkinapproach,highlycomputationalaccuracyiskept.Byusingvariousprioriestimatetechniquesfordifferentialequations,difficultycomingformnon-linearityistreated,andoptimalH^1andL^2convergenceprop-ertiesaredemonstrated.Moreover,althoughalltheexistedADGalerkinschemesusingpatchapproximationarelimitedtohaveonlyoneorderaccuracyintimeincrement,yettheschemesformulatedinthispaperhavesecondorderaccuracyinit.ThisimpliesanessentialadvancementinADGalerkinaualysis.
