Adaptive finite element approximation for a constrained optimal control problem via multi-meshes

DOI10.1007/s10915-009-9296-yzbMath1203.65099OpenAlexW2016113132MaRDI QIDQ618507

Liang Ge, Danping Yang, Wen-bin Liu

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-009-9296-y

zbMATH Keywords

a posteriori error estimatesadaptive finite element methodsoptimal control problemsmulti-meshes

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Discrete approximations in optimal control (49M25)

Related Items (11)

Convergence and quasi-optimality of an adaptive finite element method for optimal control problems with integral control constraint ⋮ Convergence and quasi-optimality based on an adaptive finite element method for the bilinear optimal control problem ⋮ A non-overlapping DDM for optimal boundary control problems governed by parabolic equations ⋮ Convergence and quasi-optimality of \(L^2\)-norms based an adaptive finite element method for nonlinear optimal control problems ⋮ Adaptive finite element approximation for an elliptic optimal control problem with both pointwise and integral control constraints ⋮ A non-overlapping DDM combined with the characteristic method for optimal control problems governed by convection-diffusion equations ⋮ Variational discretization for optimal control problems governed by parabolic equations ⋮ Convergence and superconvergence of variational discretization for parabolic bilinear optimization problems ⋮ Efficient block preconditioners for integral constrained elliptic optimal control problems with finite element approximations ⋮ A posteriori error estimates for optimal control problems constrained by convection-diffusion equations ⋮ Optimal control of viscous Burgers equation via an adaptive nonmonotone Barzilai–Borwein gradient method

Cites Work

• A posteriori error estimators for the Stokes equations
• A posteriori error estimation in finite element analysis
• On multi-mesh \(H\)-adaptive methods
• Analysis of Inexact Trust-Region SQP Algorithms
• An optimal control approach to a posteriori error estimation in finite element methods
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept
• Augmented Lagrange-SQP Methods with Lipschitz-Continuous Lagrange Multiplier Updates
• A Trust Region Method for Parabolic Boundary Control Problems
• Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
• Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods
• A posteriori error estimates for distributed convex optimal control problems
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