| [1] Adams R A and Fournier J. Sobolev Spaces[M]. Second Edition, Academic Press, New York, 2003.[2] Monk P. Finite Element Methods for Maxwell Equations[M]. Clarendon Press, Oxford, 2003.[3] Buffa A. Remarks on the discretization of some noncoercive operator with applications to heterogeneous maxwell equations[J]. SIAM J. Numer. Anal., 2005, 43(1):1-18.[4] Nédélec J. Mixed finite elements in R3[J]. Numer. Math., 1980, 35(3):315-341.[5] Arnold D N, Brezzi F and Marini L D. Unified analysis of discontinuous Galerkin methods for elliptic problems[J]. SIAM J. Numer. Anal., 2001, 39(5):1749-1779.[6] Riviére B. Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations:Theory and Implementation[M]. SIAM, 2008.[7] Duan H Y, Li S. Tan Roger C.E. and Zheng W.Y., A delta-regularization finite element method for a double curl problem with divergence-free constraint[J]. SIAM J. Numer. Anal., 2012, 50(6):3208-3230.[8] Duan H Y, Lin P and Tan Roger C E. C0 elements for generalized indefinite Maxwell's equations[J]. Numer. Math., 2012, 122(1):61-99.[9] Houston P, Perugia I, Schneebeli A and Schötzau D. Interior penalty method for indefinite timeharmonic Maxwell equations[J]. Numer. Math., 2005100(3):485-518.[10] Grote M J, Schneebeli A and Schötzau D. Interior penalty discontinuous Galerkin method for Maxwell's equations:Energy norm error estimates[J]. J. Comp. Appl. Math., 2007, 204(2):375-386.[11] Cockburn B, Li F and Shu C W. Locally divergence-free discontinuous Galerkin methods for the Maxwell equations[J]. J. Comput. Phys., 2004, 194(2):588-610.[12] Otin R. Regularized Maxwell equations and nodal finite elements for electromagnetic field computations[J]. Electromagnetics, 2010, 30(1):190-204.[13] Costabel M and Dauge M. Weighted regularization of Maxwell equations in polyhedral domains[J]. Numer. Math., 2002, 93(2):239-277.[14] Brezzi F and Fortin M. Mixed and Hybrid Finite Element Methods[M]. Springer-Verlag, NewYork, 1991.[15] Girault V and Raviart P A. Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms[M]. Springer-Verlag, Berlin, 1986.[16] Duan H Y, Lin P and Tan Roger C E. Error estimates for a vectorial second-order elliptic eigenproblem by the local L2 projected C0 finite element method[J]. SIAM J. Numer. Anal., 2013, 51(3):1678-1714.[17] Ciarlet P G. The Finite Element Method for Elliptic Problems[M]. Amsterdam:North-Holland, 1978.[18] Duan H Y, Jia F, Lin P and Tan Roger C E. The local L2 projected C0 finite element method for Maxwell problem[J]. SIAM J. Numer. Anal., 2009, 47(2):1274-1303.[19] Brenner S C and Scott L R. The Mathematical Theory of Finite Element Methods[M]. Third Edition, Springer-Verlag, New-York, 2008.[20] Clément P. Approximation by finite element functions using local regularization[J]. RAIRO Anal. Numer., 1975, 2(R-2):77-84.[21] Xue Y, Duan H Y and Zhang Q. A new and simple implementation of the element-local L2-projected continuous finite element method[J]. Appl. Math. Comput., 2014, 228:170-183.[22] Duan H Y, Tan Roger C E, Yang S Y and You C S. Computation of Maxwell singular solution by nodal-continuous elements[J]. J. Comput. Phys., 2014, 268:63-83.[23] Buffa A and Ciarlet P Jr. On traces for functional spaces related to Maxwell's equations Part Ⅱ:Hodge decompositions on the boundary of Lipschitz polyhedra and applications[J]. Math. Meth. Appl. Sci., 2001, 24(1):31-48.[24] Dhia A B, Bonnet-Ben, Hazard C and Lohrengel S. A Singular Field Method For the Solution of Maxwell's Equations in Polyhedral Domains[J]. SIAM J. Appl. Math., 1999, 59(6):2028-2044.[25] Duan H Y, Lin P, Saikrishnan P and Tan Roger C E. A least-squares finite element method for the magnetostatic problem in a multiply connected Lipschitz domain[J]. SIAM J. Numer. Anal., 2007, 45(6):2537-2563.[26] Duan H Y, Lin P and Tan Roger C E. Analysis of a continuous finite element method for H(curl, div)-elliptic interface problem[J]. Numer. Math., 2013, 123(4):671-707.[27] Boffi D, Brezzi F and Fortin M. Mixed Finite Element Methods and Applications[M]. Springer, 2013.[28] Arnold D N, Brezzi F, Cockburn B and Marini D. Discontinuous Galerkin Methods for Elliptic Problems[M]. Lect. Notes Comput. Sci. Eng., Springer, Berlin, 2000, 11:89-101. |
