TY - JOUR
T1 - Extrapolation of mixed finite element approximations for the Maxwell eigenvalue problem
AU - Yao, Changhui
AU - Qiao, Zhonghua
N1 - The first author was supported in part by NSFF P. R. China No. 10971203. The second author was supported in part by Hong Kong Baptist University Grant FRG2/09-10/034.
PY - 2011/8
Y1 - 2011/8
N2 - 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 O(h2) to O(h4) when applying the lowest order Nédélec 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.
AB - 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 O(h2) to O(h4) when applying the lowest order Nédélec 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.
KW - Asymptotic error expansion
KW - Maxwell eigenvalue problem
KW - Mixed finite element
KW - Richardson extrapolation
UR - http://www.scopus.com/inward/record.url?scp=80052216463&partnerID=8YFLogxK
U2 - 10.4208/nmtma.2011.m1018
DO - 10.4208/nmtma.2011.m1018
M3 - Journal article
AN - SCOPUS:80052216463
SN - 1004-8979
VL - 4
SP - 379
EP - 395
JO - Numerical Mathematics
JF - Numerical Mathematics
IS - 3
ER -