Mixed and hybrid Petrov-Galerkin finite element discretization for optimal control of the wave equation
type: Item
instance of: scholarly article
title: Mixed and hybrid Petrov-Galerkin finite element discretization for optimal control of the wave equation
zbMATH Open document ID: 1487.49007
published in: Numerische Mathematik
publication date: 2022-03-21T00:00:00Z
review text: The article deals with a classical problem in optimal control of partial differential equation. The dynamics is given by the wave equation with Dirichlet boundary condition, with a distributed control acting on the whole domain. After rewriting the wave equation as a first-order coupled PDE with pressure and velocity variables, the cost to be minimized is a balance between the tracking of pressure-velocity towards a reference and the \(L^2\) cost of the control. The novelty of the article is to propose a numerical method that is based on the Raviart-Thomas finite elements in space and a Petrov-Galerkin scheme. The main advantage of these choices is that the discretize-then-optimize and optimize-then-discretize procedures coincide. Convergence of the scheme is proved to be linear.
reviewed by: Francesco Rossi
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 7493702
zbMATH Keywords: optimal control
zbMATH Keywords: partial differential equations
zbMATH Keywords: wave equation
zbMATH Keywords: finite element discretization
author: Gilbert R. Peralta
author: Karl Kunisch
describes a project that uses: mfem
describes a project that uses: ARPACK
MaRDI profile type: Publication
full work available at URL: s00211-021-01258-9
OpenAlex ID: W4205468673
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DOI: 10.1007/S00211-021-01258-9
description: scientific article; zbMATH DE number 7493702