Approximation of sparse controls in semilinear equations by piecewise linear functions
type: Item
instance of: scholarly article
title: Approximation of sparse controls in semilinear equations by piecewise linear functions
zbMATH Open document ID: 1284.65074
author: Eduardo Casas
author: Gerd Wachsmuth
author: Roland Herzog
published in: Numerische Mathematik
publication date: 2012-12-20T00:00:00Z
review text: The authors consider a distributed optimal control problem defined by a semilinear elliptic differential equation where the objective functional is non-differentiable. Both the state and the controls are discretized by continuous piecewise linear functions. Then they prove the convergence of the discretization and derive error estimates for the optimal control. These are obtained by an appropriate discretization of the objective functional using a quadrature formulae. Finally, numerical examples confirm the convergence rates.
reviewed by: Basilis Kokkinis
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 6117690
zbMATH Keywords: optimal control
zbMATH Keywords: non-differentiable objective functional
zbMATH Keywords: sparse controls
zbMATH Keywords: finite element discretization
zbMATH Keywords: a priori error estimates
zbMATH Keywords: semilinear elliptic differential equation
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
describes a project that uses: CGAL
describes a project that uses: FEniCS
MaRDI profile type: Publication
full work available at URL: s00211-012-0475-7
OpenAlex ID: W1963754437
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DOI: 10.1007/S00211-012-0475-7
description: scientific article; zbMATH DE number 6117690