BIT Numerical Mathematics

, Volume 50, Issue 4, pp 781–795 | Cite as

Convergence analysis of finite element approximations of the Joule heating problem in three spatial dimensions

  • Michael J. Holst
  • Mats G. Larson
  • Axel Målqvist
  • Robert Söderlund
Open Access


In this paper we present a finite element discretization of the Joule-heating problem. We prove existence of solution to the discrete formulation and strong convergence of the finite element solution to the weak solution, up to a sub-sequence. We also present numerical examples in three spatial dimensions. The first example demonstrates the convergence of the method in the second example we consider an engineering application.


Finite element methods Joule heating problem Convergence analysis 

Mathematics Subject Classification (2000)

65N30 35J60 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Michael J. Holst
    • 1
  • Mats G. Larson
    • 2
  • Axel Målqvist
    • 3
  • Robert Söderlund
    • 2
  1. 1.Department of MathematicsUniversity of California at San DiegoLa JollaUSA
  2. 2.Department of MathematicsUmeå UniversityUmeåSweden
  3. 3.Department of Information TechnologyUppsala UniversityUppsalaSweden

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