A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations
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- by Susanne C. Brenner, Fengyan Li and Li-yeng Sung PDF
- Math. Comp. 76 (2007), 573-595 Request permission
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.References
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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
- MR Author ID: 718718
- 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
- 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.
- © Copyright 2006 American Mathematical Society
- Journal: Math. Comp. 76 (2007), 573-595
- MSC (2000): Primary 65N30, 65N15, 35Q60
- DOI: https://doi.org/10.1090/S0025-5718-06-01950-8
- MathSciNet review: 2291828