Skip to main content
SpringerLink
Log in

Numerical Approximation of Exact Controls for Waves

  • Book
  • © 2013

Overview

Authors:
  1. Sylvain Ervedoza

    1. Université Paul Sabatier & CNRS, Equipe MIP, Institut de Mathématique de Toulouse, Toulouse Cedex 9, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Enrique Zuazua

    1. BCAM-Basque Center for Applied Mathemati, Bilbao, Spain

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Devoted to fully developing and comparing continuous and the discrete approaches to the numerical approximation of controls for wave propagation phenomena
  • Provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions
  • Includes supplementary material: sn.pub/extras

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (5 chapters)

  1. Front Matter

    Pages i-xvii
    Download chapter PDF

  2. Numerical Approximation of Exact Controls for Waves

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 1-48

  3. Observability for the 1—d Finite-Difference Wave Equation

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 49-58

  4. Convergence of the Finite-Difference Method for the 1—d Wave Equation with Homogeneous Dirichlet Boundary Conditions

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 59-78

  5. Convergence with Nonhomogeneous Boundary Conditions

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 79-114

  6. Further Comments and Open Problems

    • Sylvain Ervedoza, Enrique Zuazua
    Pages 115-118

  7. Back Matter

    Pages 119-122
    Download chapter PDF
Back to top

Keywords

About this book

​​​​​​This book is devoted to fully developing and comparing the two main approaches to the numerical approximation of controls for wave propagation phenomena: the continuous and the discrete. This is accomplished in the abstract functional setting of conservative semigroups.The main results of the work unify, to a large extent, these two approaches, which yield similaralgorithms and convergence rates. The discrete approach, however, gives not only efficient numerical approximations of the continuous controls, but also ensures some partial controllability properties of the finite-dimensional approximated dynamics. Moreover, it has the advantage of leading to iterative approximation processes that converge without a limiting threshold in the number of iterations. Such a threshold, which is hard to compute and estimate in practice, is a drawback of the methods emanating from the continuous approach. To complement this theory, the book provides convergence results for the discrete wave equation when discretized using finite differences and proves the convergence of the discrete wave equation with non-homogeneous Dirichlet conditions. The first book to explore these topics in depth, "On the Numerical Approximations of Controls for Waves" has rich applications to data assimilation problems and will be of interest to researchers who deal with wave approximations.​

Authors and Affiliations

  • Université Paul Sabatier & CNRS, Equipe MIP, Institut de Mathématique de Toulouse, Toulouse Cedex 9, France

    Sylvain Ervedoza

  • BCAM-Basque Center for Applied Mathemati, Bilbao, Spain

    Enrique Zuazua

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation