Adaptive finite element approximation for an elliptic optimal control problem with both pointwise and integral control constraints

DOI10.1007/s10915-013-9790-0zbMath1311.65083OpenAlexW2010114282MaRDI QIDQ474931

Liang Ge, Ning Du, Wen-bin Liu

Publication date: 25 November 2014

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

Full work available at URL: https://doi.org/10.1007/s10915-013-9790-0

zbMATH Keywords

variational inequalitiesfinite element approximationa posteriori error estimatesoptimal control problemadaptive finite element methodnumerical resultmulti-meshes

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Numerical methods for variational inequalities and related problems (65K15)

Related Items (6)

A fast gradient projection method for a constrained fractional optimal control ⋮ On the formulation and numerical simulation of distributed-order fractional optimal control problems ⋮ Galerkin spectral approximations for optimal control problems governed by the fourth order equation with an integral constraint on state ⋮ A posteriori error estimates of \(hp\) spectral element methods for optimal control problems with \(L^2\)-norm state constraint ⋮ Galerkin spectral approximation of optimal control problems with \(L^2\)-norm control constraint ⋮ Legendre-Galerkin spectral methods for optimal control problems with integral constraint for state in one dimension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Adaptive finite element approximation for a constrained optimal control problem via multi-meshes
• A posteriori error estimators for the Stokes equations
• Constructural-theory network of conducting paths for cooling a heat generating volume
• A posteriori error estimation in finite element analysis
• On multi-mesh \(H\)-adaptive methods
• Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems
• Analysis of Inexact Trust-Region SQP Algorithms
• ERROR ESTIMATES IN THE APPROXIMATION OF OPTIMIZATION PROBLEMS GOVERNED BY NONLINEAR OPERATORS
• Variational Discretization of Parabolic Control Problems in the Presence of Pointwise State Constraints
• Finite Element Analysis of Optimal Control Problem Governed by Stokes Equations with L²-Norm State-Constraints
• Numerical Analysis of a System of Singularly Perturbed Convection-Diffusion Equations Related to Optimal Control
• 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
• Data Oscillation and Convergence of Adaptive FEM
• A Trust Region Method for Parabolic Boundary Control Problems
• Adaptive Finite Element Approximation for Distributed Elliptic Optimal Control Problems
• Second-Order Necessary and Sufficient Optimality Conditions for Optimization Problems and Applications to Control Theory
• A Convergent Adaptive Algorithm for Poisson’s Equation
• Multigrid Methods for Elliptic Optimal Control Problems with Pointwise State Constraints
• Finite Element Approximations of an Optimal Control Problem with Integral State Constraint
• A posteriori error estimates for distributed convex optimal control problems

This page was built for publication: Adaptive finite element approximation for an elliptic optimal control problem with both pointwise and integral control constraints