Numerical Approximation of Exact Controls for Waves

• Main Authors: Ervedoza, Sylvain. (Author), Zuazua, Enrique. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Series: SpringerBriefs in Mathematics,
• Subjects: Mathematics.; Differential equations, partial.; Systems theory.; Algorithms.; Numerical analysis.; Approximations and Expansions.; Partial Differential Equations.; Systems Theory, Control.; Numerical Analysis.; Applications of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4614-5808-1

 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.