二次非线性最优控制问题的混合有限元解的后验误差估计

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1、Á`¯3ÆÚó§A^¥k~¿Â,Ùê{ïÄÉ<2'5.k{´8)û`¯~^{,¯õÆö3ù¡þïÄ.©¥,·?ØaÉ5ý.§åg`¯·Ük)Ø©Û.·æ^kRaviart-Thomas,Brezzi-Douglas-Marini½Brezzi-Douglas-Fortin-Marini·ÜméGCþÚGCþ?1%C,Ó

2、^©¡~ê¼êéCþ?1%C.éuRT,BDM½öBDFM,·ÏEþ¼ê£6þ¤Helmholtz©),¥mþØ,nÜù(,5`¯Ø

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,·Äå8Ǒ«~^æa.,?Ú©Û5`¯Ø,Ü·Ø«f.3©ê¢¥,·æ^ý^Ýf{5)¯,æ^ØÓ©éGCþÚCþ?1%C.òØ«fǑ«f.¢²,g·A{´«~k{.':5`¯:·Ük%C:Ø.IAbstractOptimalcontrolproblemsareplayinganimportantroleinscientificcomputationsandengineeringapplications,andmuchattentionhasbee

4、npaidtoitsnumericalmethods.Recentlythefiniteelementmethodseemstobethemostwidelyusedmethodincomputingoptimalcontrolproblems,andtherelevantliteratureishuge.Inthiswork,weinvestigatetheposteriorierrorestimatesforthemixedfiniteele-mentapproximationofquadraticoptimalcontrolproble

5、mgovernedbynonlinearellipticequation.Thestateandco-stateareapproximatedbythek-thRaviart-Thomas,Brezzi-Douglas-MariniandBrezzi-Douglas-Fortin-Marinimixedfiniteelementspacesandthecon-trolisapproximatedbypiecewiseconstantfunctions.Ourresultsarebasedontheapprox-imationforbotht

6、hestatevariablesandthecontrolvariable.WederiveaerrorestimatesforsomeintermediateerrorsfortheRT,theBDMandtheBDFMmixedmethod,ouranal-ysisreliedonadecompositionofthefluxfunctionsinthespiritofageneralizedHemholtzdecomposition,thenweobtainaposteriorierrorestimatesfortheclassofo

7、ptimalcontrolproblems.Wearethenabletoderiveaposteriorierrorestimates,whichcanguidethemeshrefinementprocessintheadaptiveanalysis.Weconsiderthemostusefultypeofconstraints,aposteriorierrorestimatorsareestablishedfortheconstrainedoptimalcon-trolproblems.Inourexperiments,theopt

8、imizationproblemweresolvednumericallybyapreconditionedprojectionalgorithm,weusedifferentmeshesfortheapproximationofthestateandthecontrol,andusetheposteriorierrorestimatorsasthemeshrefinementindicator.Thenitisclearthattheadaptivefiniteelementmethodismoreefficient.Keywords:nonli

9、nearoptimalcontrolproblems;mixedfiniteelementapprox-imation;posteriorierrorestimates.IIÆÆØ©5(²