Article

Numerische Mathematik

, Volume 109, Issue 4, pp 509-533

First online:

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

  • S. C. BrennerAffiliated withDepartment of Mathematics and Center for Computation and Technology, Louisiana State University Email author 
  • , J. CuiAffiliated withDepartment of Mathematics, Louisiana State University
  • , F. LiAffiliated withDepartment of Mathematical Sciences, Rensselaer Polytechnic Institute
  • , L.-Y. SungAffiliated withDepartment of Mathematics, Louisiana State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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 P 1 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 L 2 norm are established on graded meshes. The theoretical results are confirmed by numerical experiments.

Keywords

Curl–curl and grad-div problem Nonconforming finite element methods Maxwell equations

Mathematics Subject Classification (2000)

65N30 65N15 35Q60