ThisarticledescribesalocalerrorestimatorforGlimm'sschemeforhyperbolicsystemsofconservationlawsandusesittoreplacetheusualrandomchoiceinGlimm'sschemebyanoptimalchoice.Asaby-productofthelocalerrorestimator,theprocedureprovidesaglobalerrorestimatorthatisshownnumericallytobeaveryaccurateestimateoftheerrorinL1(R)foralltimes.Althoughthereispartialmathematicalevidencefortheerrorestimatorproposed,atthisstagetheerrorestimatormustbeconsideredad-hoc.Nonetheless,theerrorestimatorissimpletocompute,relativelyinexpensive,withoutadjustableparametersandatleastasaccurateasotherexistingerrorestimators.Numericalexperimentsin1-DforBurgers'equationandforEuler'ssystemareperformedtomeasuretheasymptoticaccuracyoftheresultingschemeandoftheerrorestimator.
