Journal of Scientific Computing

, Volume 55, Issue 3, pp 738–754 | Cite as

An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations

  • S. C. BrennerEmail author
  • J. Gedicke
  • L.-Y. Sung


Recently a new numerical approach for two-dimensional Maxwell’s equations based on the Hodge decomposition for divergence-free vector fields was introduced by Brenner et al. In this paper we present an adaptive P 1 finite element method for two-dimensional Maxwell’s equations that is based on this new approach. The reliability and efficiency of a posteriori error estimators based on the residual and the dual weighted-residual are verified numerically. The performance of the new approach is shown to be competitive with the lowest order edge element of Nédélec’s first family.


Adaptivity Error estimators Finite element method Hodge decomposition Maxwell’s equations 



The bulk of this paper was written while the second author enjoyed the hospitality of the Center for Computation and Technology at Louisiana State University.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Computation & TechnologyLouisiana State UniversityBaton RougeUSA
  2. 2.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany

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