{rfName}
Nu

Indexed in

License and Use

Icono OpenAccess

Citations

67

Altmetrics

Analysis of institutional authors

Castro, CarlosCorresponding Author

Share

June 9, 2019
Publications
>
Article
Sí

Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square

Publicated to: IMA JOURNAL OF NUMERICAL ANALYSIS. 28 (1): 186-214 - 2008-01-01 28(1), DOI: 10.1093/imanum/drm012

Authors:

Castro, Carlos; Micu, Sorin; Munch, Arnaud;
[+]

Affiliations

Grupo de Ingeniería Estructural. Universidad Politécnica de Madrid - Author
Univ Craiova, Fac Matemat Informat, Dolj 200585, Romania - Author
Univ Franche Comte, CNRS, UMR 6623, Lab Math Besancon, F-25030 Besancon, France - Author
Univ Politecn Madrid, Dept Matemat & Informat Aplicadas Ingn Civil, Escuela Tecn Super Ingn Caminos Canales & Puertos, Madrid 28040, Spain - Author
See more

Abstract

This paper studies the numerical approximation of the boundary control for the wave equation in a square domain. It is known that the discrete and semi-discrete models obtained by discretizing the wave equation with the usual finite-difference or finite-element methods do not provide convergent sequences of approximations to the boundary control of the continuous wave equation as the mesh size goes to zero. Here, we introduce and analyse a new semi-discrete model based on the space discretization of the wave equation using a mixed finite-element method with two different basis functions for the position and velocity. The main theoretical result is a uniform observability inequality which allows us to construct a sequence of approximations converging to the minimal L-2-norm control of the continuous wave equation. We also introduce a fully discrete system, obtained from our semi-discrete scheme, for which we conjecture that it provides a convergent sequence of discrete approximations as both h and Delta t, the time discretization parameter, go to zero. We illustrate this fact with several numerical experiments.
[+]

Keywords

ControllabilityExact controllabilityNumerical approximation of controlsObservabilitySpace semi-discretizationsWave equation

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal IMA JOURNAL OF NUMERICAL ANALYSIS due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2008, it was in position 23/175, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics, Applied.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2026-04-25:

  • WoS: 29
  • Scopus: 38
[+]

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2026-04-25:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 7 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
  • Assignment of a Handle/URN as an identifier within the deposit in the Institutional Repository: https://oa.upm.es/2922/

As a result of the publication of the work in the institutional repository, statistical usage data has been obtained that reflects its impact. In terms of dissemination, we can state that, as of

  • Views: 545
  • Downloads: 730
[+]

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: France; Oman; Rumanía.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (CASTRO BARBERO, CARLOS MANUEL) .

the author responsible for correspondence tasks has been CASTRO BARBERO, CARLOS MANUEL.

[+]