Space-Time Finite Element Discretization of Parabolic Optimal Control Problems with Energy Regularization

DOI10.1137/20M1332980zbMath1467.65094arXiv2004.09504OpenAlexW3135041483MaRDI QIDQ5855637

Ulrich Langer, Huidong Yang, Fredi Tröltzsch, Olaf Steinbach

Publication date: 19 March 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.09504

zbMATH Keywords

discretization error estimatesparabolic optimal control problemsspace-time finite element methods

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Existence theories for optimal control problems involving partial differential equations (49J20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Discrete approximations in optimal control (49M25) PDE constrained optimization (numerical aspects) (49M41)

Related Items (9)

Simultaneous space-time finite element methods for parabolic optimal control problems ⋮ Optimization problems for PDEs in weak space-time form. Abstracts from the workshop held March 5--10, 2023 ⋮ Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations ⋮ Numerical modeling and open-source implementation of variational partition-of-unity localizations of space-time dual-weighted residual estimators for parabolic problems ⋮ Least-squares finite elements for distributed optimal control problems ⋮ Space-Time Finite Element Methods for Distributed Optimal Control of the Wave Equation ⋮ Space-time methods for time-dependent partial differential equations. Abstracts from the workshop held February 6--12, 2022 ⋮ Unstructured Space-Time Finite Element Methods for Optimal Control of Parabolic Equations ⋮ Robust discretization and solvers for elliptic optimal control problems with energy regularization

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