Crank--Nicolson Time Stepping and Variational Discretization of Control-Constrained Parabolic Optimal Control Problems

DOI10.1137/14099680XzbMath1319.49045arXiv1403.3010MaRDI QIDQ5254015

Michael Hinze, Nikolaus von Daniels, Morten Vierling

Publication date: 8 June 2015

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

Full work available at URL: https://arxiv.org/abs/1403.3010

zbMATH Keywords

heat equationerror estimatesfinite elementscontrol constraintsparabolic optimal control problemsCrank-Nicolson time steppingvariational control discretization

Mathematics Subject Classification ID

Numerical methods involving duality (49M29) Numerical methods based on necessary conditions (49M05) Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

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Cites Work

• Finite element solution of diffusion problems with irregular data
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Third order convergent time discretization for parabolic optimal control problems with control constraints
• Crank--Nicolson Schemes for Optimal Control Problems with Evolution Equations
• The semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalization
• A Priori Error Analysis of the Petrov–Galerkin Crank–Nicolson Scheme for Parabolic Optimal Control Problems
• Optimization with PDE Constraints
• A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control Constraints
• A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part II: Problems with Control Constraints
• Unnamed Item

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