AnewmethodbasedontheanisotropictensorforcefiniteelementandTaylor-Galerkinfiniteelementispresentedinthepresentpaper.Itsapplicationtotwo-dimensionalviscoustransonicflowinturbomachineryimprovestheconver-gencerateandstabilityofcalculation,andtheresultsobtainedagreewellwiththeexperimentalmeasurements.