Robust finite element discretization and solvers for distributed elliptic optimal control problems

DOI10.1515/cmam-2022-0138arXiv2207.04664OpenAlexW4321217671MaRDI QIDQ6088295

Richard Löscher, Huidong Yang, Olaf Steinbach, Ulrich Langer

Publication date: 16 November 2023

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04664

zbMATH Keywords

finite element discretizationelliptic optimal control problemsrobust error estimates\(L^2\) regularizationrobust solvers

Mathematics Subject Classification ID

Numerical methods based on necessary conditions (49M05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Iterative numerical methods for linear systems (65F10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Preconditioners for iterative methods (65F08) PDE constrained optimization (numerical aspects) (49M41)

Related Items (4)

Optimization problems for PDEs in weak space-time form. Abstracts from the workshop held March 5--10, 2023 ⋮ Editorial. Recent advances in finite element methods ⋮ Space-Time Finite Element Methods for Distributed Optimal Control of the Wave Equation ⋮ An adaptive finite element method for distributed elliptic optimal control problems with variable energy regularization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iterative solution of large sparse systems of equations
• Applications of multilevel methods to practical problems
• On the robustness and optimality of algebraic multilevel methods for reaction-diffusion type problems
• An efficient preconditioning method for state box-constrained optimal control problems
• On the convergence of a multigrid method for linear reaction-diffusion problems
• Theory and practice of finite elements.
• Robust discretization and solvers for elliptic optimal control problems with energy regularization
• Analysis of iterative methods for saddle point problems: a unified approach
• A new approximation of the Schur complement in preconditioners for PDE-constrained optimization
• A New Analysis of Block Preconditioners for Saddle Point Problems
• Preconditioning discretizations of systems of partial differential equations
• Block-triangular preconditioners for PDE-constrained optimization
• Nonstandard Norms and Robust Estimates for Saddle Point Problems
• Numerical solution of saddle point problems
• Symmetric Indefinite Preconditioners for Saddle Point Problems with Applications to PDE-Constrained Optimization Problems
• Multigrid Methods for PDE Optimization
• A Preconditioning Technique for Indefinite Systems Resulting from Mixed Approximations of Elliptic Problems
• Solution of Sparse Indefinite Systems of Linear Equations
• Convergence of Some Iterative Methods for Symmetric Saddle Point Linear Systems
• Error bounds for tikhonov regularization in hilbert scales
• Regularization error estimates for distributed control problems in energy spaces
• The Mathematical Theory of Finite Element Methods
• Transforming smoothers for PDE constrained optimization problems

This page was built for publication: Robust finite element discretization and solvers for distributed elliptic optimal control problems