Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems

From MaRDI portal
Publication:4706241

DOI10.1137/S0363012901389342zbMath1034.49031OpenAlexW2014303698WikidataQ61773180 ScholiaQ61773180MaRDI QIDQ4706241

Ruo Li, Tao Tang, Wen-bin Liu, He-Ping Ma

Publication date: 19 June 2003

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0363012901389342




Related Items

Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-ConstraintA Posteriori Error Estimates for $hp$ Spectral Element Approximation of Elliptic Control Problems with Integral Control and State ConstraintsA priorianda posteriorierror estimates for the method of lumped masses for parabolic optimal control problemsUsing mesh adaption for the identification of a spatial field of material propertiesA priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problemsA priori error estimates and superconvergence of P02-P1 mixed finite element methods for elliptic boundary control problemsConvergence and regularization results for optimal control problems with sparsity functionalA fast gradient projection method for a constrained fractional optimal controlOptimal convergence of finite element approximation to an optimization problem with PDE constraint*Conjugate gradient-boundary element solution for distributed elliptic optimal control problemsSuperconvergence of splitting positive definite mixed finite element for parabolic optimal control problemsError estimates of mixed finite element methods for quadratic optimal control problemsModel Reduction by Adaptive Discretization in Optimal ControlAdaptive Symmetric Interior Penalty Galerkin Method for Boundary Control ProblemsUnnamed ItemFinite element approximation to optimal Dirichlet boundary control problem: a priori and a posteriori error estimatesAnalysis of an Adaptive Finite Element Method for Recovering the Robin CoefficientUnified discontinuous Galerkin finite element methods for second order Dirichlet boundary control problemA two-layer Crank-Nicolson linear finite element methods for second-order hyperbolic optimal control problemsAdaptive finite element approximation of optimal control problems with the integral fractional LaplacianA data‐driven optimal control method for endoplasmic reticulum membrane compartmentalization in budding yeast cellsA posteriori error estimates of a DG method for optimal control problems governed by the transport equationError estimates of \textit{hp} spectral element methods in nonlinear optimal control problemAna posteriorierror analysis of adaptive finite element methods for distributed elliptic control problems with control constraintsStochastic discontinuous Galerkin methods for robust deterministic control of convection-diffusion equations with uncertain coefficientsError bounds for a Dirichlet boundary control problem based on energy spacesMixed finite element method for a second order Dirichlet boundary control problemOptimal control and numerical adaptivity for advection–diffusion equationsA posteriori error estimators for optimal distributed control governed by the first-order linear hyperbolic equation: DG methodSolving ill-posed control problems by stabilized finite element methods: an alternative to Tikhonov regularizationFully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface ModelsL-error estimates of higher order mixed finite element approximations for elliptic optimal control problemsError Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic EquationsIdentification of a Corroded Boundary and Its Robin CoefficientAdaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraintsSuperconvergence of mixed finite element methods for optimal control problemsSome error estimates of finite volume element method for parabolic optimal control problemsA posteriorierror estimates for mixed finite element approximation of nonlinear quadratic optimal control problemsAdaptive Finite Element Methods for Parameter Identification ProblemsAdaptive characteristic finite element approximation of convection–diffusion optimal control problemsOne-shot methods in function space for PDE-constrained optimal control problemsSuperconvergence of quadratic optimal control problems by triangular mixed finite element methodsGoal Oriented Mesh Adaptivity for Mixed Control-State Constrained Elliptic Optimal Control ProblemsEstimating the control error in discretized PDE-constrained optimizationAdaptive finite element discretization in PDE-based optimizationInterpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problemsA Posteriori Error Estimates of Mixed Methods for Parabolic Optimal Control ProblemsAn adaptive finite element algorithm for parabolic optimal control problemsA posteriori error estimates of spectral method for optimal control problems governed by parabolic equationsA posteriori error estimates of constrained optimal control problem governed by convection diffusion equationsFourier Finite Volume Element Method for Two Classes of Optimal Control Problems Governed by Elliptic PDEs on Complex Connected DomainA new marking strategy for the adaptive finite element approximation of optimal control constrained problemsA Posteriori Error Estimation in PDE-constrained Optimization with Pointwise Inequality ConstraintsConvergence of an adaptive finite element method for distributed flux reconstructionA Posteriori Error Estimates of Semidiscrete Mixed Finite Element Methods for Parabolic Optimal Control ProblemsError estimates of expanded mixed methods for optimal control problems governed by hyperbolic integro-differential equationsThe optimisation of the mesh in first-order systems least-squares methodsOn multi-mesh \(H\)-adaptive methodsA priori and posteriori error estimates of Legendre Galerkin spectral methods for general elliptic optimal control problemsAdaptive Finite Elements for Optimally Controlled Elliptic Variational Inequalities of Obstacle TypeNew a posteriori \(L^\infty(L^2)\) and \(L^2(L^2)\)-error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems.Error estimates of pseudostress-velocity MFEM for optimal control problems governed by Stokes equationsA posteriori error estimates for control problems governed by nonlinear elliptic equations in \(hp\)-FEMA posteriori error estimates of spectral method for nonlinear parabolic optimal control problemError estimates and superconvergence of mixed finite element methods for fourth order hyperbolic control problemsError estimates in \(L^2\) and \(L^\infty\) norms of finite volume method for the bilinear elliptic optimal control problemError estimates of variational discretization for semilinear parabolic optimal control problemsA frequency-dependent \(p\)-adaptive technique for spectral methods\textit{A priori} error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: \textit{hp}-streamline diffusion discontinuous Galerkin methodImmersed finite elements for optimal control problems of elliptic PDEs with interfacesConvergence of adaptive nonconforming finite element method for Stokes optimal control problemsSuperconvergence of semidiscrete splitting positive definite mixed finite elements for hyperbolic optimal control problemsConvergence and quasi-optimality of an adaptive finite element method for optimal control problems with integral control constraintA posteriori error estimation and adaptivity for elliptic optimal control problems with state constraintsAdaptive finite element approximation for a class of parameter estimation problemsVariational discretization for parabolic optimal control problems with control constraintsA posteriori error estimates for an optimal control problem of laser surface hardening of steelError estimates of semidiscrete mixed methods for optimal control problems governed by parabolic integro-differential equationsAdaptive multilevel correction method for finite element approximations of elliptic optimal control problemsOn gradient-type optimization method utilizing mixed finite element approximation for optimal boundary control problem governed by bi-harmonic equationFunctional approach to a posteriori error estimation for elliptic optimal control problems with distributed controlConvergence and quasi-optimality of an adaptive finite element method for optimal control problems on \(L^{2}\) errorsFinite element approximation for a class of parameter estimation problemsA priori error estimates for optimal control problems governed by transient advection-diffusion equationsAdaptive finite element approximation for a constrained optimal control problem via multi-meshesError estimates and superconvergence of mixed finite element methods for convex optimal control problemsAdaptive finite element methods for the identification of elastic constantsMulti-mesh adaptive finite element algorithms for constrained optimal control problems governed by semi-linear parabolic equationsA priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equationsA priori error estimates of mixed finite element methods for general semilinear elliptic optimal control problemsAdaptive mixed finite element methods for parabolic optimal control problemsFinite element preconditioning on spectral element discretizations for coupled elliptic equationsSharp a posteriori error estimates for optimal control governed by parabolic integro-differential equationsGoal-oriented a posteriori error estimation for Dirichlet boundary control problemsA fuzzy system based active set algorithm for the numerical solution of the optimal control problem governed by partial differential equationSuperconvergence of RT1 mixed finite element approximations for elliptic control problemsError analysis for optimal control problem governed by convection diffusion equations: DG methodOptimal control problem of the two-dimensional modified anomalous subdiffusion equation with discontinuous Galerkin approximationEquivalent a posteriori error estimates for elliptic optimal control problems with \(L^1\)-control cost\(HN\)-adaptive spectral element discretization of optimal control problems for environmental applicationsError estimates and superconvergence of a mixed finite element method for elliptic optimal control problemsA posteriori error estimates of mixed finite element methods for general optimal control problems governed by integro-differential equationsA posteriori error control for distributed elliptic optimal control problems with control constraints discretized by \(hp\)-finite elementsConvergence and quasi-optimality of \(L^2\)-norms based an adaptive finite element method for nonlinear optimal control problemsConstants within error estimates for Legendre-Galerkin spectral approximations of control-constrained optimal control problemsThe constants in a posteriori error indicator for state-constrained optimal control problems with spectral methodsAdaptive finite element approximation for an elliptic optimal control problem with both pointwise and integral control constraintsAn adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle typeSuperconvergence analysis and two-grid algorithms of pseudostress-velocity MFEM for optimal control problems governed by Stokes equationsA dual weighted residual method for an optimal control problem of laser surface hardening of steelFast intersections on nested tetrahedrons (FINT): An algorithm for adaptive finite element based distributed parameter estimationAdaptive finite element methods for the identification of distributed parameters in elliptic equation\(L^{\infty}\)-error estimates of rectangular mixed finite element methods for bilinear optimal control problemSuperconvergence and a posteriori error estimates of splitting positive definite mixed finite element methods for elliptic optimal control problemsAdaptive finite element method for Dirichlet boundary control of elliptic partial differential equationsAdaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equationsA posteriori error estimates of recovery type for distributed convex optimal control problemsNew elliptic projections and a priori error estimates of \(H^1\)-Galerkin mixed finite element methods for optimal control problems governed by parabolic integro-differential equationsExtended finite element methods for optimal control problems governed by Poisson equation in non-convex domainsConjugate gradient-boundary element solution using multiple reciprocity method for distributed elliptic optimal control problemsA Nitsche-extended finite element method for distributed optimal control problems of elliptic interface equationsA \(C^0\) interior penalty method for the Dirichlet control problem governed by biharmonic operatorA priori and a posteriori error analysis of edge stabilization Galerkin method for the optimal control problem governed by convection-dominated diffusion equationA posteriori error estimates for mixed finite element solutions of convex optimal control problemsAdaptive finite element method for elliptic optimal control problems: convergence and optimalityError analysis of variational discretization solving temperature control problemsError estimates of triangular mixed finite element methods for quasilinear optimal control problemsA priori and a posteriori error estimates of \(H^1\)-Galerkin mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equationsA posteriori error estimates for \(hp\) finite element solutions of convex optimal control problemsAdaptive mixed finite element methods for nonlinear optimal control problemsCharacteristic mixed finite element approximation of transient convection diffusion optimal control problemsA mixed multiscale finite element method for convex optimal control problems with oscillating coefficientsA priori and a posteriori error estimates of \(H^1\)-Galerkin mixed finite element methods for elliptic optimal control problemsOn the formulation and numerical simulation of distributed-order fractional optimal control problemsAdaptive edge element approximation of \(H(\mathrm{curl}\)-elliptic optimal control problems with control constraintsMoving mesh finite element methods for an optimal control problem for the advection-diffusion equationAdaptive optimal control approximation for solving a fourth-order elliptic variational inequalityMoving mesh discontinuous Galerkin method for hyperbolic conservation lawsAdaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problemsResidual-type a posteriori error analysis of HDG methods for Neumann boundary control problemsAdaptive virtual element method for optimal control problem governed by general elliptic equationFull-discrete adaptive FEM for quasi-parabolic integro-differential PDE-constrained optimal control problemVariational discretization for optimal control problems governed by parabolic equationsConvergence and superconvergence of variational discretization for parabolic bilinear optimization problemsAdaptive variational discretization approximation method for parabolic optimal control problemsError estimates of finite volume method for Stokes optimal control problem\textit{A posteriori} error estimates of characteristic mixed finite elements for convection-diffusion control problemsAdaptive Hermite spectral methods in unbounded domainsLegendre-Galerkin spectral methods for optimal control problems with integral constraint for state in one dimensionSuperconvergence of fully discrete rectangular mixed finite element methods of parabolic control problemsDiscontinuous Galerkin method for a distributed optimal control problem governed by a time fractional diffusion equationA posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methodsA priori and a posteriori error analysis of \textit{hp} spectral element discretization for optimal control problems with elliptic equationsLocal a posteriori error analysis of finite element method for parabolic boundary control problemsLocal a posteriori error estimates for boundary control problems governed by nonlinear parabolic equationsA posteriori error estimates for optimal control problems constrained by convection-diffusion equationsResidual-based \textit{a posteriori} error estimates for \textit{hp} finite element solutions of semilinear Neumann boundary optimal control problemsMixed discontinuous Galerkin time-stepping method for semilinear parabolic optimal control problemsA posteriori error estimates of mixed finite element solutions for fourth order parabolic control problemsA posteriori error estimates of the lowest order Raviart-Thomas mixed finite element methods for convective diffusion optimal control problems