Extrapolation of the Nédélec element for the Maxwell equations by the mixed finite element method

In this paper, we use the integral-identity argument to obtain asymptotic error expansions for the mixed finite element approximation of the Maxwell equations on a rectangular mesh. The extrapolation method is applied to improve the accuracy of the approximation via an interpolation postprocessing technique. With the extrapolation, the approximation accuracy can be improved from O(h) to O(h ⁴) in the L ²-norm. Illustrative numerical results are given to demonstrate the higher order accuracy of the extrapolation method. This research was supported by the National Natural Science Foundation of China (No.10471103), Social Science Foundation of the Ministry of Education of China (06JA630047), Tianjin Natural Science Foundation (07JCYBJC14300).