dc.contributor.author Castro, C. dc.contributor.author Zuazua, E. dc.date.accessioned 2017-02-21T08:18:21Z dc.date.available 2017-02-21T08:18:21Z dc.date.issued 2011-12-31 dc.identifier.issn 0025-5718 dc.identifier.uri http://hdl.handle.net/20.500.11824/596 dc.description.abstract We consider the problem of flux identification for 1-d scalar conservation laws formulating it as an optimal control problem. We introduce a new optimization strategy to compute numerical approximations of minimizing fluxes. We first prove the existence of minimizers. We also prove the convergence of discrete minima obtained by means of monotone numerical approximation schemes, by a Γ-convergence argument. Then we address the problem of developing efficient descent algorithms. We first consider and compare the existing two possible approaches. The first one, the so-called discrete approach, based on a direct computation of gradients in the discrete problem and the so-called continuous one, where the discrete descent direction is obtained as a discrete copy of the continuous one. When optimal solutions have shock discontinuities, both approaches produce highly oscillating minimizing sequences and the effective descent rate is very weak. As a remedy we adapt the method of alternating descent directions that uses the recent developments of generalized tangent vectors and the linearization around discontinuous solutions, introduced by the authors, in collaboration with F. Palacios, in the case where the control is the initial datum. This method distinguishes descent directions that move the shock and those that perturb the profile of the solution away from it. As we shall see, a suitable alternating combination of these two classes of descent directions allows building more efficient and faster descent algorithms. dc.format application/pdf dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject 1-d scalar conservation laws dc.subject Alternating descent method dc.subject Flux identification dc.subject Numberical approximation dc.subject Optimal control dc.title Flux identification for 1-d scalar conservation laws in the presence of shocks dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1090/S0025-5718-2011-02465-8 dc.relation.publisherversion https://www.scopus.com/inward/record.uri?eid=2-s2.0-79960620619&doi=10.1090%2fS0025-5718-2011-02465-8&partnerID=40&md5=1f7ee9fb125a361c8d6c7230b177a80a dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Mathematics of Computation en_US
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