On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation

DOI10.1016/j.crma.2018.02.011zbMath1401.65112OpenAlexW2791860002MaRDI QIDQ1747409

Philip Trautmann, Boris Vexler, Alexander Zlotnik

Publication date: 8 May 2018

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2018.02.011

zbMATH Keywords

error estimatesfinite element methodinitial-boundary value problemcost functional1D wave equationvector measuresoptimal control problemsmeasure-valued functionsstability boundregularized Galerkin method

Mathematics Subject Classification ID

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Discrete approximations in optimal control (49M25)

Cites Work

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• A sharp form of the Sobolev trace theorems
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• Sparse initial data identification for parabolic PDE and its finite element approximations
• Optimal Control of the Undamped Linear Wave Equation with Measure Valued Controls
• Parabolic control problems in space-time measure spaces
• Some questions in the optimal control of distributed systems
• Parabolic Control Problems in Measure Spaces with Sparse Solutions
• Measure Valued Directional Sparsity for Parabolic Optimal Control Problems

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