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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations


Authors: Susanne C. Brenner, Fengyan Li and Li-yeng Sung
Journal: Math. Comp. 76 (2007), 573-595
MSC (2000): Primary 65N30, 65N15, 35Q60
Published electronically: December 27, 2006
MathSciNet review: 2291828
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Abstract: A new numerical method for computing the divergence-free part of the solution of the time-harmonic Maxwell equations is studied in this paper. It is based on a discretization that uses the locally divergence-free Crouzeix-Raviart nonconforming $ P_1$ vector fields and includes a consistency term 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.


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Additional Information

Susanne C. Brenner
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Address at time of publication: Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803
Email: brenner@math.lsu.edu

Fengyan Li
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Address at time of publication: Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180
Email: lif@rpi.edu

Li-yeng Sung
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
Address at time of publication: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sung@math.lsu.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01950-8
PII: S 0025-5718(06)01950-8
Keywords: Time-harmonic Maxwell equations, nonconforming finite element methods
Received by editor(s): August 8, 2005
Received by editor(s) in revised form: April 19, 2006
Published electronically: December 27, 2006
Additional Notes: The work of the first author was supported in part by the National Science Foundation under Grant No. DMS-03-11790.
Article copyright: © Copyright 2006 American Mathematical Society