Extrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem |
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Authors: | Changhui Yao Zhonghua Qiao |
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Institution: | 1. Department of Mathematics, Zhengzhou University, Zhengzhou, China 2. Institute for Computational Mathematics & Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong |
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Abstract: | In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalue approximations are obtained.Based on the asymptotic error expansion formulas,the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from θ(h2) to θ(h4) when applying the lowest order Nédé1ec mixed finite element and a nonconforming mixed finite element.To our best knowledge,this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation.Numerical experiments are provided to demonstrate the theoretical results. |
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Keywords: | Maxwell eigenvalue problem mixed finite element asymptotic error expansion Richardson extrapolation |
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