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77.FushengLuo,HehuXie,MantingXieandFeiXu,Adaptivetime-steppingalgorithmsformolecularbeamepitaxy:Basedonenergyorroughness,AppliedMathematicsLetters,99(2020),105991.
76.HehuXie,LeiZhang,HoumanOwhadi,Fasteigenpairscomputationwithoperatoradaptedwaveletsandhierarchicalsubspacecorrections,SIAMJournalonNumericalAnalysis,57(6)(2019),2519-2550.
75.QilongZhai,HehuXie,RanZhangandZhiminZhang,AccelerationofweakGalerkinmethodsfortheLaplacianeigenvalueproblem,JournalofScientificComputing,79(2019),914-934.
74.NingZhang,FeiXuandHehuXie,AnefficientmultigridmethodforgroundstatesolutionofBose-Einsteincondensates,InternationalJournalofNumericalAnalysisandModeling,16(5)(2019),789-903.
(Contribution:inthispaper,wesolveanonlineareigenvalueproblemwiththeabsoluteasymptoticallyoptimalcomplexityindependentfromthenonlinearity.)
73.HehuXie,MantingXieandNingZhang,Anefficientmultigridmethodforsemilinearellipticequation,JournalofNumericalMethodsandComputerApplications,40(2)(2019),143-160.
谢和虎、谢满庭、张宁，一种求解半线性椭圆问题的快速多重网格法，数值计算与计算机应用，40（2）（2019），143-160.
72.QilongZhai,HehuXie,RanZhangandZhiminZhang,TheweakGalerkinmethodforellipticeigenvalueproblems,COmmun.Comput.Phys.,26(1)(2019),160-191.
71.Chun'guangYou,HehuXieandXuefengLiu,GuaranteedeigenvalueboundsfortheStekloveigenvalueproblem,SIAMJ.Numer.Anal.,57(3)(2019),1395-1410.
70.MeilingYue,HehuXieandMantingXie,Acascadicmultigridmethodfornonsymmetriceigenvalueproblem,AppliedNumericalMathematics,146(2019),55-72.
69.QichenHong,HehuXie,MeilingYueandNingZhang,Fullycomputableerrorboundsforeigenvalueproblem,InternationalJournalofNumericalAnalysisandModeling,15(2018),2560-276.
68.GuanghuiHu,HehuXieandFeiXu,AmultilevelcorrectionadaptivefiniteelementmethodforKohn–Shamequation,JournalofComputationalPhysics,355(15),(2018),436-449.
67.Y.He,Y.Li,H.Xie,C.YouandN.Zhang,AmultilevelNewton'smethodforeigenvalueproblems,ApplicationsofMathematics,63(3)(2018),281-303.
66.M.Xie,H.XieandX.Liu,ExplicitlowerboundsforStokeseigenvalueproblemsbyusingnonconformingfiniteelements,JapanJournalofIndustrialandAppliedMathematics,35(1)(2018),335-354.
65.Y.Di,HehuXieandX.Yin,AnisotropicmeshesandstabilizationparameterdesignoflinearSUPGmethodfor2Dconvection-dominatedconvection-diffusionequations,JournalofScientificComputing,76(1)(2018),48-68.
64.Q.Hong,H.Xie,M.YueandN.Zhang,Fullycomputableerrorboundsforeigenvalueproblem,InternationalJournalofNumericalAnalysisandModleing,15(1-2)(2018),260–276.
63.FeiXuandHehuXie,Afullmultigridmethodforsemilinearellipticequation,ApplicationsofMathematics,62(3)(2017),225-241.
62.HehuXieandXinmingWu,Amultilevelcorrectionmethodforinteriortransmissioneigenvalueproblem,JournalofScientificComputing,72(2017),586-604.
61.WeiGong,HehuXieandNingningYan,Adaptivemultilevelcorrectionmethodforfiniteelementapproximationsofellipticoptimalcontrolproblems,JournalofScientificComputing,72(2017),820-841.
60.XiaJi,YingxiaXiandHehuXie,Nonconformingfiniteelementmethodforthetransmissioneigenvalueproblem,AdvancesinAppliedMathematicsandMechanics,9(1)(2017),92-103.
59.XiaoleHan,HehuXieandFexiXu,Acascadicmultigridmethodforeigenvalueproblem,JournalofComputationalMathematics,35(1)(2017),75-91.
58.HehuXieandM.Xie,AmultigridmethodforgroundstatesolutionofBose-Eineteincondensates,Commun.Comput.Phys.,19(3)(2016),648-662.
57.S.Jia,HehuXie,M.XieandF.Xu,Afullmultigridmethodfornonlineareigenvalueproblems,SciChinaMath,59(2016),2037–2048.
56.F.Luo,T.TangandHehuXie,Parameter-freetimeadaptivitybasedonenergyevolutionfortheCahn-Hilliardequation,Commun.Comput.Phys.,19(05)(2016),1542-1563.
55.H.Chen,HehuXieandF.Xu,Afullmultigridmethodforeigenvalueproblems,JournalofComputationalPhysics,322(2016),747-759.
54.XiaoleHan,YuLi,HehuXieandChunguangYou,Localandparallelfiniteelementalgorithmbasedonmultileveldiscretizationforeigenvalueproblems,InternationalJournalofNumericalAnalysis&Modeling,13(1)(2016),73-89.
53.ZhonghuaQiao,TaoTangandHehuXie,Erroranalysisofamixedfiniteelementmethodformolecularbeamepitaxymodel,SIAMJ.Numer.Anal.,53(1)(2015）,184–205.
52.HehuXieandTaoZhou,AmultilevelfiniteelementmethodforFredholmintegraleigenvalueproblems,JournalofComputationalPhysics,303(2015),173-184
51.HehuXie,Atypeofmulti-levelcorrectionschemeforeigenvalueproblemsbynonconformingfiniteelementmethods,BITNumericalMathematics,55(4)(2015),1243-1266.
50.HongtaoChen,YunhuiHe,YuLiandHehuXie,Amultigridmethodforeigenvalueproblemsbasedonshifted-inversepowertechnique.EuropeanJournalofMathematics,1(1)(2015),207-228.
49.XiaoleHan,YuLiandHehuXie,AmultilevelcorrectionmethodforStekloveigenvalueproblembynonconformingfiniteelementmethods,NumericalMathematics:Theory,MethodsandApplications,8(03)(2015),383-405.
48.HehuXieandXiaoboYin,AccelerationofstabilizedfiniteelementdiscretizationsfortheStokeseigenvalueproblem,Adv.Comput.Math.,41(2015),799–812
47.谢和虎,非线性特征值问题的多重网格算法,中国科学：数学，45（8）（2015），1193-1204.
HehuXie,Amultigridmethodfornonlineareigenvalueproblems(inChinese),SciSinMath,45(2015),1193-1204
46.QunLin,HehuXieandFeiXu,Multilevelcorrectionadaptivefiniteelementmethodforsemilinearellipticequation,ApplicationofMathematics,60(5)(2015),527-550.
45.WeiGong,HehuXie,NingningYan,Amultilevelcorrectionmethodforoptimalcontrolsofellipticequation,SIAMJ.Sci.Comput.,37(5)（2015),A2198-A2221,2015.
44.QunLin,FushengLuoandHehuXie,AmultilevelcorrectionmethodforStokeseigenvalueproblemsanditsapplication,MathematicalMethodsintheAppliedSciences,38(18)(2015),4540-4552.
43.ShanghuiJia,FushengLuoandHehuXie,APosteriorErrorAnalysisfortheNonconformingDiscretizationofStokesEigenvalueProblem,ActaMathematicaSinica,EnglishSeries,30(6)(2014),949–967.
42.X.Feng,Z,WenandHehuXie,Accelerationoftwo-gridstabilizedmixedfiniteelementmethodfortheStokeseigenvalueproblem,ApplicationofMathematics,59(6)(2014),615-630.
41.HehuXie,AtypeofmultilevelmethodfortheStekloveigenvalueproblem,IMAJ.Numer.Anal.,34(2)(2014),592-608.
40.HehuXie,Amultigridmethodforeigenvalueproblem,JournalofComputationalPhysics,274(1),2014,pages550-561.
39.XiaJi,JiguangSunandHehuXie,AmultigridmethodforHelmholtztransmissioneigenvalueproblems,JournalofScientificComputing,60(2),pages:276-294,2014.
38.QunLin,FushengLuoandHehuXie,Aposteriorierrorestimatorandlowerboundofanonconformingfiniteelementmethod,JournalofComputationalandAppliedMathematics,256(1),pages243-254,2014.
37.QunLinandHehuXie,Amulti-levelcorrectionschemeforeigenvalueproblems,MathematicsofComputation,84(291)(2015),71-88.
36.XiaoboYinandHehuXie,Metrictensorsfortheinterpolationerroranditsgradientin$L^p$norm,JournalofComputationalPhysics,256(1),Pages:543-562,2014.
35.QunLin,HehuXieandJinchaoXu,LowerBoundsoftheDiscretizationforPiecewisePolynomials,Math.Comp.,83(2014),1-13.
34.YuLi,QunLinandHehuXie,Aparallelmethodforpopulationbalanceequationsbasedonthemethodofcharacteristics,ProceedingsoftheInternationalConferenceApplicationsofMathematics,2013,pp.140-149.
33.RanZhang,BenxiZhuandHehuXie,SpectralmethodsforweaklysingularVolterraintegralequationswithpantographdelays，FrontiersofMathematicsinChina,Vol.8,Issue2,2013,pp281-299
32.TaoTang,HehuXieandXiaoboYin,High-OrderConvergenceofSpectralDeferredCorrectionMethodsonGeneralQuadratureNodes,JournalofScientificComputingVolume56,Issue1,2013,pp1-13
31.QiumeiHuang,HehuXieandHermannBrunner,The$hp$DiscontinuousGalerkinMethodforDelayDifferentialEquationswithNonlinearVanishingDelay,SIAMJ.Sci.Comput.,35(3),2013,A1604–A1620.
30.QinLi,QunLinandHehuXie,NonconformingfiniteelementapproximationsoftheStekloveigenvalueproblemanditslowerboundapproximations,ApplicationsofMathematics,Volume58,Issue2,2013,pp129-151.
29.ShanghuiJia，HongtaoChenandHehuXie,Aposteriorierrorestimatorforeigenvalueproblemsbymixedfiniteelementmethod,ScienceChinaMathematics,Volume56,Issue5,2013,pp887-900
28.QunLinandHehuXie,Extrapolationofthefiniteelementmethodongeneralmeshes,InternationalJournalofNumericalAnalysisandModelingComputingandInformation,Vol.10,Number1,2013,pp.139-153.
27.QunLinandHehuXie,RecentresultsonLowerboundsofeigenvalueproblemsbynonconformingfiniteelementmethods,InverseProblemsandImaging,Volume7,No.3,2013,795-811.
26.F.Luo,QunLinandHehuXie(谢和虎),ComputingthelowerandupperboundsofLaplaceeigenvalueproblem:bycombiningconformingandnonconformingfiniteelementmethods,ScienceChinaMathematics,Volume55,Issue5,pp1069-1082,2012.
25.QunLinandHehuXie(谢和虎),ASuperconvergenceresultformixedfiniteelementapproximationsoftheeigenvalueproblem,ESAIM:MathematicalModellingandNumericalAnalysis,Volume46/Issue04,pp797-812,2012.
24、QunLinandHehuXie(谢和虎),AmultilevelcorrectiontypeofadaptivefiniteelementmethodforStekloveigenvalueproblems,ProceedingsoftheInternationalConferenceApplicationsofMathematics2012,pp.134-143.
23.Q.LinandH.Xie,Theasymptoticlowerboundsofeigenvalueproblemsbynonconformingfiniteelementmethods,MathematicsinPracticeandTheory,42(11)(2012),219–226.(InChinesewithEnglishtitleandabstract)
22.H.Xie,R.ZhangandH.Brunner,CollocationMethodsforGeneralVolterraFunctionalIntegralEquationswithVanishingDelays,SIAMJournalonScientificComputing,33(6)(2011),3303-3332.
21.QunLinandHehuXie,AnobservationonAubin-NitscheLemmaanditsapplications,MathematicsinPracticeandTheory,41(17)(2011),247-258.(InChinese,Englishtitleandabstract)
20.QunLinandHehuXie,Atypeoffiniteelementgradientrecoverymethodbasedonvertex-edge-faceinterpolation:Therecoveryrechniqueandsuperconvergenceproperty,EastAsianJournalonAppliedMathematics,1(3)(2011),248-263.
19.S.Jia,H.XieandX.Yin,Atypeoffiniteelementgradientrecoverymethodbasedonvertex-edgeinterpolation,MathematicsinPracticeandTheory,41(6)(2011),239-243.(InChinese,Englishtitleandabstract)
18.Q.Huang,H.XieandH.Brunner,SuperconvergenceofadiscontinuousGalerkinsolutionsfordelaydifferentialequationsofpantographtype,SIAMJournalonScientificComputing，33(5)(2011),2664–2684.
17.QunLinandHehuXie,SuperconvergencemeasurementforGeneralmeshesbylinearfiniteelementmethod,MathematicsinPracticeandTheory,41(1)(2011),138-152.(InChinese,Englishtitleandabstract)
16.N.Ahmed,G.Matthies,L.TobiskaandH.Xie,DiscontinuousGalerkintimesteppingwithlocalprojectionstabilizationfortransientconvection-diffusion-reactionproblems，Comput.MethodsAppl.Mech.Engrg.,200(2011),1747-1756.
15.H.Eichel,L.TobiskaandH.Xie,SuperclosenessandsuperconvergenceofstabilizedloworderfiniteelementdiscretizationsoftheStokesproblem,MathematicsofComputation,80(274)(2011),697–722.
14.H.Brunner,Q.HuangandH.Xie,DiscontinuousGalerkinmethodsfordelaydifferentialequationsofpantographtype,SIAMJ.NUMER.ANAL.,Vol.48,No.5,pp.1944–1967,2010.
13.Q.Lin,H.Xie,F.Luo,Y.LiandY.Yang,Stokeseigenvalueapproximationsfrombelowwithnonconformingmixedfiniteelementmethods,MathematicsinPracticeandTheory,40(19)(2010),157-168.(InChinese,Englishtitleandabstract)
12.H.Brunner,HehuXieandR.Zhang,Analysisofcollocationsolutionsforaclassoffunctionalequationswithvanishingdelays,IMAJournalofNumericalAnalysis,31(2011),698-718.
11.QunLinandHehuXie,Newexpansionsofnumericaleigenvaluefor$-\Deltau=\lambda\rhou$bylinearfiniteelementondifferenttriangularmeshes,InternationalJournalofInformationandSystemsSciences,6(1)(2010),10-34
10.QunLinandHehuXie,AsymptoticerrorexpansionandRichardsonextrapolationofeigenvalueapproximationsforsecondorderellipticproblemsbythemixedfiniteelementmethod,AppliedNumericalMathematics,59(8)(2009),1884—1893.
9.Q.HuangandHehuXie,SuperconvergenceofGalerkinsolutionsforHammersteinequations,InternationalJournalofNumericalAnalysis&Modeling,2009，Volume6,Number4,Pages:696-710.
8.H.Chen,S.JiaandHehuXie,PostprocessingandhigherorderconvergenceforthemixedfiniteelementapproximationsoftheStokeseigenvalueproblems,ApplicationofMathematics,54(3)(2009),237-250.
7.S.Jia,HehuXie,X.YinandS.Gao,ApproximationandeigenvalueextrapolationofStokeseigenvalueproblembynonconformingfiniteelementmethods,ApplicationsofMathematics,54(1)(2009),1-15.
6.HehuXieandS.Jia,Extrapolationforthesecondorderellipticproblemsbymixedfiniteelementmethodsinthreedimensions,InternationalJournalofNumericalAnalysisandModeling,5(1)(2008),112-131.
5.S.Jia,HehuXie,X.YinandS.Gao,Approximationandeigenvalueextrapolationofbiharmoniceigenvalueproblembynonconformingfiniteelementmethods,NumericalMethodsforPartialDifferentialEquations,24(2),435-448,2008.
4.X.Yin,HehuXie,S.JiaandS.Gao,Asymptoticexpansionsandextrapolationsofeigenvaluesforthestokesproblembymixedfiniteelementmethods,JournalofComputationalandAppliedMathematics,215(1)(2008),127-141
3.HehuXie,ExtrapolationoftheNédélecelementfortheMaxwellequationsbythemixedfiniteelementmethod,AdvancesinComputationalMathematics,29(2)(2008),135-145.
2.HehuXieandS.Gao,Superconvergenceoftheleast-squaresmixedfiniteelementapproximationsforthesecondorderellipticproblems,InternationalJournalofInformationandSystemsSceiences,Vol.3(2)(2007),277-282.
1.V.ShaidurovandHehuXie,Richardsonextrapolationforeigenvalueofdiscretespectralproblemongeneralmesh,ComputationalTechnologies,Vol.12No.3(2007),24-37.
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