Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations

DOI10.1007/s10589-014-9718-0zbMath1320.65102arXiv1311.6282OpenAlexW2045526409MaRDI QIDQ2350867

Johannes Pfefferer, Klaus Krumbiegel

Publication date: 25 June 2015

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6282

zbMATH Keywords

superconvergencenumerical experimentpostprocessinggraded meshesfinite element error estimatessemilinear elliptic Neumann boundary control problem

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) 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) Semilinear elliptic equations (35J61)

Related Items

Numerical analysis for the pure Neumann control problem using the gradient discretisation method ⋮ Virtual element method for elliptic Neumann boundary optimal control problem ⋮ The Gradient Discretization Method for Optimal Control Problems, with Superconvergence for Nonconforming Finite Elements and Mixed-Hybrid Mimetic Finite Differences ⋮ Optimal Control of Partial Differential Equations ⋮ Error estimates for the finite element approximation of bilinear boundary control problems ⋮ Morley FEM for a distributed optimal control problem governed by the von Kármán equations ⋮ Numerical approximation of control problems of non-monotone and non-coercive semilinear elliptic equations ⋮ Finite element error estimates on the boundary with application to optimal control

Cites Work

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• On saturation effects in the Neumann boundary control of elliptic optimal control problems
• Finite element error estimates for Neumann boundary control problems on graded meshes
• Approximation of a class of optimal control problems with order of convergence estimates
• Error estimates for the numerical approximation of boundary semilinear elliptic control prob\-lems
• Approximate quasi-Newton methods
• Error estimates for the numerical approximation of Neumann control problems
• Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems
• Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
• A variational discretization concept in control constrained optimization: The linear-quadratic case
• Error estimates for the numerical approximation of a semilinear elliptic control problem
• Uniform convergence of the FEM applications to state constrained control problems
• Optimal control in non-convex domains: a priori discretization error estimates
• Local mesh refinement for the discretization of Neumann boundary control problems on polyhedra
• Second Order Analysis for Optimal Control Problems: Improving Results Expected From Abstract Theory
• Boundary Control of Semilinear Elliptic Equations with Pointwise State Constraints
• Error estimates for linear-quadratic control problems with control constraints
• $L^\infty$-Estimates for Approximated Optimal Control Problems
• Superconvergence Properties for Optimal Control Problems Discretized by Piecewise Linear and Discontinuous Functions
• Direct Methods in the Theory of Elliptic Equations
• On the approximation of the solution of an optimal control problem governed by an elliptic equation
• The Neumann problem on Lipschitz domains
• Reduced SQP Methods for Parameter Identification Problems
• Primal-Dual Strategy for Constrained Optimal Control Problems
• Second Order Optimality Conditions for Semilinear Elliptic Control Problems with Finitely Many State Constraints
• Superconvergence Properties of Optimal Control Problems
• Optimal Control Problems with Partially Polyhedric Constraints
• Primal-Dual Active Set Strategy for a General Class of Constrained Optimal Control Problems
• Finite element error estimates on the boundary with application to optimal control