Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • Boundary observability for the space semi-discretizationsof the 1 – d wave equation

  • Juan Antonio Infante, Enrique Zuazua
  • Journal:
    ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 2 / March 1999
    Published online by Cambridge University Press:
    15 August 2002, pp. 407-438
    Print publication:
    March 1999

  • We consider space semi-discretizations of the 1-d wave equation in a boundedinterval with homogeneous Dirichlet boundary conditions. We analyze the problemof boundary observability, i.e., the problem of whether the total energy ofsolutions can be estimated uniformly in terms of the energy concentrated on theboundary as the net-spacing h → 0. We prove that, due to the spurious modesthat the numerical scheme introduces at high frequencies, there is no such auniform bound. We prove however a uniform bound in a subspace of solutionsgenerated by the low frequencies of the discrete system. When h → 0 thisfinite-dimensional spaces increase and eventually cover the whole space. Wethus recover the well-known observability property of the continuous systemas the limit of discrete observability estimates as the mesh size tends tozero.We consider both finite-difference and finite-element semi-discretizations.