Numerische Mathematik

, Volume 109, Issue 4, pp 509–533

A nonconforming finite element method for a two-dimensional curl–curl and grad-div problem

Article

DOI: 10.1007/s00211-008-0149-7

Cite this article as:
Brenner, S.C., Cui, J., Li, F. et al. Numer. Math. (2008) 109: 509. doi:10.1007/s00211-008-0149-7

Abstract

A numerical method for a two-dimensional curl–curl and grad-div problem is studied in this paper. It is based on a discretization using weakly continuous P1 vector fields and includes two consistency terms involving the jumps of the vector fields across element boundaries. Optimal convergence rates (up to an arbitrary positive \({\epsilon}\)) in both the energy norm and the L2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

Keywords

Curl–curl and grad-div problemNonconforming finite element methodsMaxwell equations

Mathematics Subject Classification (2000)

65N3065N1535Q60

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Computation and TechnologyLouisiana State UniversityBaton RougeUSA
  2. 2.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  3. 3.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA