Mortar element coupling between global scalar and local vector potentials to solve eddy current problems

  • Y. Maday
  • F. Rapetti
  • B. I. Wohlmuth


The TΩ formulation of the magnetic field has been introduced in many papers for the approximation of the magnetic quantities modeled by the eddy current equations. This decomposition allows us to use a scalar function in the main part of the computational domain, reducing the use of vector quantities in the conducting parts. We propose here to approximate these two quantities on different and non-matching grids so as. e.g., to tackle a problem where the conducting part can move in the global domain. The connection between the two grids is managed with mortar element tools. The numerical analysis is presented, resulting in error bounds for the solution.


Bilinear Form Interpolation Operator Homogeneous Dirichlet Boundary Condition Harmonic Extension Ellipticity Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Albanese, R., Rubinacci, G. (1990): Formulation of the eddy-current problem. IEE Proc. A 137, 16–22Google Scholar
  2. [2]
    Ammari, H., Buffa, A., Nédélec, J.-C. (2000): Ajustification of eddy currents model for the Maxwell equations. SIAM J. Appl. Math. 60, 1805–1823MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Bernardi, C., Maday, Y., Patera, A. (1994): A new nonconforming approach to domain decomposition: the mortar element method. In: Brézis, H., Lions, J.-L. (eds.): Nonlinear partial differential equations and their applications. Collége de France Seminar. Vol XI. Longman, Harlow, UK, pp. 13–51Google Scholar
  4. [4]
    Bossavit, A. (1998): Computational electromagnetism. Variational formulations, complementarity, edge elements. Academic Press, San Diego, CAMATHGoogle Scholar
  5. [5]
    Brezzi, F., Fortin, M. (1991): Mixed and hybrid finite element methods. Springer, New YorkMATHCrossRefGoogle Scholar
  6. [6]
    Dubois, F. (1990): Discrete vector potential representation of a divergence-free vector field in three-dimensional domains: numerical analysis of a model problem. SIAM J. Numer. Anal. 27, 1103–1141MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Girault, V., Raviart, P.-A. (1986): Finite element methods for Navier-Stokes equations. Springer, BerlinMATHCrossRefGoogle Scholar
  8. [8]
    Maday, Y., Rapetti, F., Wohlmuth, B.I. (2002): Coupling between scalar and vector potentials by the mortar element method. C. R. Math. Acad. Sci. Paris 334, 933–938MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Nédélec, J.-C. (1980): Mixed finite elements in R 3. Numer. Math. 35, 315–341MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    Wohlmuth, B.I. (2001): Discretization methods and iterative solvers based on domain decomposition. (Lecture Notes in Computational Sciences and Engineering, vol. 17). Springer, BerlinMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia 2003

Authors and Affiliations

  • Y. Maday
    • 1
  • F. Rapetti
    • 2
  • B. I. Wohlmuth
    • 3
  1. 1.Laboratoire J.-L. LionsCNRS & Paris 6 UniversityParisFrance
  2. 2.Laboratoire J. A. DieudonnéUMR CNRSNiceFrance
  3. 3.Mathematisches Institut AUniversität StuttgartStuttgartGermany

Personalised recommendations