Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept

Authors:
Roland Becker;Hartmut Kapp;Rolf Rannacher
Affiliations:
-;-;-
Venue:
SIAM Journal on Control and Optimization
Year:
2000

Citing 0
Cited 26

Fast Iterative Solution of Saddle Point Problems in Optimal Control Based on Wavelets

Computational Optimization and Applications
A posteriori error estimates for control problems governed by nonlinear elliptic equations

Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Some aspects of adaptive grid technology related to boundary and interior layers

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on boundary and interior layers - computational and asymptotic methods (BAIL 2002)
Fast iterative solution of elliptic control problems in wavelet discretization

Journal of Computational and Applied Mathematics
Recovery type superconvergence and a posteriori error estimates for control problems governed by Stokes equations

Journal of Computational and Applied Mathematics
A Posteriori Error Estimates of Recovery Type for Distributed Convex Optimal Control Problems

Journal of Scientific Computing
A posteriori error estimates for mixed finite element solutions of convex optimal control problems

Journal of Computational and Applied Mathematics
Conjugate gradient-boundary element solution using multiple reciprocity method for distributed elliptic optimal control problems

Applied Numerical Mathematics
A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

Journal of Scientific Computing
Adaptive Finite Element Approximation for a Constrained Optimal Control Problem via Multi-meshes

Journal of Scientific Computing
A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints

Computational Optimization and Applications
Adaptive finite element methods for mixed control-state constrained optimal control problems for elliptic boundary value problems

Computational Optimization and Applications
A characteristic finite element method for optimal control problems governed by convection-diffusion equations

Journal of Computational and Applied Mathematics
A posteriori error estimates for a finite element discretization of interior point methods for an elliptic optimization problem with state constraints

Computational Optimization and Applications
Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology

Applied Numerical Mathematics
A posteriori error estimates for optimal distributed control governed by the evolution equations

Applied Numerical Mathematics
A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints

Journal of Scientific Computing
Optimization under adaptive error control for finite element based simulations

Computational Mechanics
Error analysis for optimal control problem governed by convection diffusion equations: DG method

Journal of Computational and Applied Mathematics
Reduced Basis Method and A Posteriori Error Estimation for Parametrized Linear-Quadratic Optimal Control Problems

SIAM Journal on Scientific Computing
Fluid-structure interactions using different mesh motion techniques

Computers and Structures
Goal-Oriented Adaptivity in Pointwise State Constrained Optimal Control of Partial Differential Equations

SIAM Journal on Control and Optimization
Adaptive Multilevel Inexact SQP Methods for PDE-Constrained Optimization

SIAM Journal on Optimization
Space-Time Adaptive Wavelet Methods for Optimal Control Problems Constrained by Parabolic Evolution Equations

SIAM Journal on Control and Optimization
Reduced Basis Method and Error Estimation for Parametrized Optimal Control Problems with Control Constraints

Journal of Scientific Computing
A posteriori error estimates for an optimal control problem of laser surface hardening of steel

Advances in Computational Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by elliptic partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates. These are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error. In this case, the computed state and costate variables can be used as sensitivity factors multiplying the local cell-residuals in the error estimators. This results in a generic and simple algorithm for mesh adaptation within the optimization process. This method is developed and tested for simple boundary control problems in semiconductor models.