@article{8b55a1b8cf6e4320971d3c0cd767e1a2,

title = "Computation of Maxwell singular solution by nodal-continuous elements",

abstract = "In this paper, we propose and analyze a nodal-continuous and H1-conforming finite element method for the numerical computation of Maxwell's equations, with singular solution in a fractional order Sobolev space H r(Ω), where r may take any value in the most interesting interval (0, 1). The key feature of the method is that mass-lumping linear finite element L2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of L2(Ω) space. We shall use the nodal-continuous linear finite elements, enriched with one element bubble in each element, to approximate the singular and non-H1 solution. Discontinuous and nonhomogeneous media are allowed in the method. Some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method.",

keywords = "Eigenvalue problem, Interface problem, Maxwell's equations, Nodal-continuous element",

author = "Duan, {Huo Yuan} and Tan, {Roger C.E.} and Yang, {Suh Yuh} and You, {Cheng Shu}",

note = "Funding Information: The authors would like to thank two anonymous referees for their valuable comments and suggestions that improved the presentation of this paper. The work of Huo-Yuan Duan was partially supported by the National Natural Science Foundation of China under the grants 11071132 and 11171168 , the Research Fund for the Doctoral Program of Higher Education of China under grants 20100031110002 and 20120031110026 , the Scientific Research Foundation for Returned Scholars, Ministry of Education of China , and the Wuhan University start-up fund from the Fundamental Research Funds for the Central Universities . The work of Suh-Yuh Yang was partially supported by the National Science Council Taiwan under the grant NSC 101-2115-M-008-008-MY2 . ",

year = "2014",

month = jul,

day = "1",

doi = "10.1016/j.jcp.2014.02.044",

language = "???core.languages.en_GB???",

volume = "268",

pages = "63--83",

journal = "Journal of Computational Physics",

issn = "0021-9991",

}