Finite element approximation of sparse parabolic control problems

We study the finite element approximation of an optimal control problem governed by a semilinear partial differential equation and whose objective function includes a term promoting space sparsity of the solutions. We prove existence of solution in the absence of control bound constraints and provid...

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Bibliographic Details
Authors: Casas Rentería, Eduardo|||0000-0002-8364-9416, Mateos Alberdi, Mariano, Rosch, Arnd
Format: article
Publication Date:2017
Country:España
Institution:Universidad de Cantabria (UC)
Repository:UCrea Repositorio Abierto de la Universidad de Cantabria
Language:English
OAI Identifier:oai:repositorio.unican.es:10902/12165
Online Access:http://hdl.handle.net/10902/12165
Access Level:Open access
Keyword:Optimal control
Semilinear parabolic equations
Sparse solutions
Finite element approximation
Error estimates
Description
Summary:We study the finite element approximation of an optimal control problem governed by a semilinear partial differential equation and whose objective function includes a term promoting space sparsity of the solutions. We prove existence of solution in the absence of control bound constraints and provide the adequate second order sufficient conditions to obtain error estimates. Full discretization of the problem is carried out, and the sparsity properties of the discrete solutions, as well as error estimates, are obtained.