Skip to main content


Weitere Artikel dieser Ausgabe durch Wischen aufrufen

01.09.2018 | Ausgabe 3/2018

Calcolo 3/2018

Convergence of a lowest-order finite element method for the transmission eigenvalue problem

Calcolo > Ausgabe 3/2018
Jessika Camaño, Rodolfo Rodríguez, Pablo Venegas
Wichtige Hinweise
This research was partially supported by Projects Fondecyt 1180859 and 11160186 and by Basal Project, CMM, Universidad de Chile.


The transmission eigenvalue problem arises in scattering theory. The main difficulty in its analysis is the fact that, depending on the chosen formulation, it leads either to a quadratic eigenvalue problem or to a non-classical mixed problem. In this paper we prove the convergence of a mixed finite element approximation. This approach, which is close to the Ciarlet–Raviart discretization of biharmonic problems, is based on Lagrange finite elements and is one of the less expensive methods in terms of the amount of degrees of freedom. The convergence analysis is based on classical abstract spectral approximation result and the theory of mixed finite element methods for solving the stream function–vorticity formulation of the Stokes problem. Numerical experiments are reported in order to assess the efficiency of the method.

Bitte loggen Sie sich ein, um Zugang zu diesem Inhalt zu erhalten

Über diesen Artikel

Weitere Artikel der Ausgabe 3/2018

Calcolo 3/2018 Zur Ausgabe

Premium Partner