Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 46, Issue 1, Pages 1-19Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-010-9406-x
Keywords
Nonconforming mixed finite element; Superconvergence; Extrapolation; Time-harmonic Maxwell's equations
Categories
Funding
- Hong Kong Baptist university [FRG/08-09/II-35]
- NSFF P.R. China [10971203]
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In this paper, a nonconforming mixed finite element approximating to the three-dimensional time-harmonic Maxwell's equations is presented. On a uniform rectangular prism mesh, superclose property is achieved for electric field E and magnetic filed H with the boundary condition Exn=0 by means of the asymptotic expansion. Applying postprocessing operators, a superconvergence result is stated for the discretization error of the postprocessed discrete solution to the solution itself. To our best knowledge, this is the first global superconvergence analysis of nonconforming mixed finite elements for the Maxwell's equations. Furthermore, the approximation accuracy will be improved by extrapolation method.
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