Inthispaper,weconsiderthelocaldiscontinuousGalerkinmethod(LDG)forsolv-ingsingularlyperturbedconvection-diffusionproblemsinone-andtwo-dimensionalset-tings.TheexistenceanduniquenessoftheLDGsolutionsareverified.Numericalex-perimentsdemonstratethatitseemsimpossibletoobtainuniformsuperconvergencefornumericalfluxesunderuniformmeshes.Thankstotheimplementationoftwo-typedif-ferentanisotropicmeshes,i.e.,theShishkinandanimprovedgrademeshes,theuniform2p+1-ordersuperconvergenceisobservednumericallyforbothone-dimensionalandtwo-dimensionalcases.
