个人简介

严宁宁，女，1955/4/6出生，正高级。 教育背景 1982年，毕业于沈阳工业大学应用数学专业； 1987年，获西安交通大学计算数学专业硕士学位； 1990年，获中国科学院计算数学与科学工程计算研究所计算数学专业博士学位； 工作简介 1990年起至今，在中国科学院数学与系统科学研究院系统科学研究所工作，现任中国科学院数学与系统科学研究院研究员，博士生导师。

研究领域

微分方程数值解及最优控制问题的数值方法

科研项目 参加国家重点基础研究发展规划项目(973)：材料计算设计与性能预测基础问题 自然科学基金（面上）项目：最优控制问题的数值模拟方法 参加自然科学基金（重点）项目：数学物理中若干非线性问题的数值解法,负责子项目：有限元后验误差估计及自适应有限元方法

近期论文

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学术论文 Adaptivefiniteelementmethodforellipticoptimalcontrolproblems:convergenceandoptimality Inthispaperweconsidertheconvergenceanalysisofadaptivefiniteelementmethodforellipticoptimalcontrolproblemswithpointwisecontrolconstraints.Weusevariationaldiscretizationconcepttodiscretizethecontrolvariableandpiecewiselinearandcontinuousfiniteelementstoapproximatethestatevariable.Basedonthewell-establishedconvergencetheoryofAFEMforellipticboundaryvalueproblems,werigorouslyprovetheconvergenceandquasi-optimalityofAFEMforoptimalcontrolproblemswithrespecttothestateandadjointstatevariables,byusingtheso-calledperturbationargument.Numericalexperimentsconfirmourtheoreticalanalysis. Finiteelementapproximationsofparabolicoptimalcontrolproblemswithcontrolsactingonalowerdimensionalmanifold Thispaperisdevotedtothestudyoffiniteelementapproximationstoparabolicoptimalcontrolproblemswithcontrolsactingonalowerdimensionalmanifold.Themanifoldcanbeapoint,acurve,orasurfacewhichmaybeindependentoftimeorevolveinthetimehorizon,andisassumedtobestrictlycontainedinthespacedomain.Atfirst,weobtainthefirstorderoptimalityconditionsforthecontrolproblemsandthecorrespondingregularityresults.Then,forthecontrolproblemsweconsiderthefullydiscretefiniteelementapproximationsbasedonthepiecewiseconstantdiscontinuousGalerkinschemefortimediscretizationandpiecewiselinearfiniteelementsforspacediscretization,andvariationaldiscretizationtothecontrolvariable.Apriorierrorestimatesarefinallyobtainedforthefullydiscretizedcontrolproblemsandsupportedbynumericalexamples. MultiscaleApproachforOptimalDesigninConductivityofCompositeMaterials Thispaperdiscussesthemultiscaleapproachforoptimaldesigninconductivityofcompositematerials.Thehomogenizationmethodandthemultiscaleasymptoticmethodarepresented.Theassociatednumericalalgorithmsandtheconvergenceanalysisareprovided.Finally,numericalexamplesarecarriedouttoconfirmthevalidityofthealgorithm. Amultilevelcorrectionmethodforoptimalcontrolsofellipticequation Weproposeinthispaperamultilevelcorrectionmethodtosolveoptimalcontrolproblemsconstrainedbyellipticequationswiththefiniteelementmethod.Inthisscheme,solvinganoptimizationproblemonthefinestfiniteelementspaceistransformedintoaseriesofsolutionsoflinearboundaryvalueproblemsbythemultigridmethodonmultilevelmeshesandaseriesofsolutionsofoptimizationproblemsonthecoarsestfiniteelementspace.Ourproposedscheme,insteadofsolvingalargescaleoptimizationprobleminthefinestfiniteelementspace,solvesonlyaseriesoflinearboundaryvalueproblemsandtheoptimizationproblemsinaverylowdimensionalfiniteelementspace,andthuscanimprovetheoverallefficiencyofthesolutionofoptimalcontrolproblemsgovernedbyPDEs. ApproximationsofEllipticOptimalControlProblemswithControlsActingonaLowerDimensionalManifold Inthispaper,westudyfiniteelementapproximationstosomeellipticoptimalcontrolproblemswithcontrolsactingonalowerdimensionalmanifoldwhichcanbeapoint,acurve,orasurface.Weusepiecewiselinearfiniteelementstoapproximatestatevariables,whileutilizingthevariationaldiscretizationtoapproximatecontrolvariables.Wederiveseveralapriorierrorestimatesforoptimalcontrolsfromdifferentcasesdependingonthedimensionsofthecomputationaldomainandthemanifoldwherecontrolsact.Weendsupwithextensivenumericalexperimentswhichconfirmourtheoreticalfindings. 发表著作 有限元超收敛及后验误差估计,SuperconvergenceAnalysisandaPosterioriErrorEstimationinFiniteElementMethods,SciencePress,2008-08 PDE最优控制问题的自适应有限元方法,AdaptiveFiniteElementMethodsforOptimalControlGovernedbyPDEs,SciencePress,2008-11 椭圆方程有限元整体超收敛及其应用,GlobalSuperconvergenceofFiniteElementMethodsforEllipticEquationsandItsApplications,科学出版社,2012-06