FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS

(整期优先)网络出版时间:2002-06-16
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Anewhigh-ordertime-steppingfiniteelementmethodbaseduponthehigh-ordernumericalintegrationformulaisformulatedforSobolevequations,whosecomputationsconsistofaniterationprocedurecoupledwithasystemoftwoellipticequations.Theoptimalandsuperconvergenceerrorestimatesforthisnewmethodarederivedbothinspaceandintime.Also,aclassofnewerrorestimatesofconvergenceandsuperconvergenceforthetime-continuousfiniteelementmethodisdemonstratedinwhichtherearenotimederivativesoftheexactsolutioninvolved,suchthattheseestimatescanbeboundedbythenormsoftheknowndata.Moreover,someusefula-posteriorierrorestimatorsaregivenonthebasisofthesuperconvergenceestimates.