TY - JOUR
T1 - Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
AU - Huang, Yunqing
AU - Li, Jichun
AU - Yang, Wei
AU - Sun, Shuyu
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Partially supported by the NSFC Key Project 11031006 and Hunan Provincial NSF Project 10JJ7001.Supported by National Science Foundation Grant DMS-0810896.Supported by Hunan Education Department Key Project 10A117.Supported by KAUST Faculty Baseline Research Fund.
PY - 2011/9
Y1 - 2011/9
N2 - Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.
AB - Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.
UR - http://hdl.handle.net/10754/561859
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999111004530
UR - http://www.scopus.com/inward/record.url?scp=80052678472&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2011.07.025
DO - 10.1016/j.jcp.2011.07.025
M3 - Article
SN - 0021-9991
VL - 230
SP - 8275
EP - 8289
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 22
ER -