简介:TherestartedFOMmethodpresentedbySimoncini[7]accordingtothenaturalcollinearityofallresidualsisanefficientmethodforsolvingshiftedsystems,whichgeneratesthesameKrylovsubspacewhentheshiftsarehandledsimultaneously.However,restartingslowsdowntheconvergence.WepresentapracticalmethodforsolvingtheshiftedsystemsbyaddingsomeRitzvectorsintotheKrylovsubspacetoformanaugmentedKrylovsubspace.NumericalexperimentsillustratethattheaugmentedFOMapproach(restartedversion)canconvergemorequicklythantherestartedFOMmethod.
简介:ThepurposeofthispaperistostudythesuperconvergencepropertiesofRitz-Volterraprojection.ThroughconstructionanewtypeofGreenfunctionandmakinguseofitspropertiesandtheprincipleofduality,thepaperprovesthattheRitz-Volterraprojectiondefinedonr-1orderfiniteelementspacesofLagrangetypeinoneandtwospacevariablecasespossessesO(h2r~2)orderandO(h4+1|Inh|)ordernodalsuperconvergence,respectively,andthesametypeofsuperconver-genceresultsaredemonstratedforthesemidiscretefinitedementapproximatesolutionsofSoboleve-quations.
简介:ThepurposeofthispaperistostudythestabilityandapproximationpropertiesofRitz-Volterraprojection.ThroughconstructinganewtypeofGreenfunctionsandmakinguseofvariouspropertiesandestimatesrelatedwiththefunctions,weprovethattheRitz-Volterraprojectiondefinedonthefinite-dimensionalsubspaceS_hofH_o~1possessestheW_p~1-stabilityandtheoptimalapproximationpropertiesinW_p~1andL_pfor2≤p≤∞.Ourresults,inthispaper,canbeappliedtothefiniteelementapproximationsformanyevolutionequationssuchasparabolicandhyperbolicintegrodifferentialequations,Sobolevequationsandvisco-elasticity,etc.