@article{b3ad70f277af4e12be02c5c7f537388f,
title = "C-0 elements for generalized indefinite Maxwell equations",
abstract = "In this paper we develop the C (0) finite element method for a generalized curlcurl-grad div indefinite Maxwell problem in a Lipschitz domain such as nonconvex polygon for which the solution of the problem may be nonsmooth and only have the H (r) regularity for some r < 1. The ingredients of our method are that two 'mass-lumping' L (2) projectors are applied to curl and div operators in the problem and that C (0) linear element or isoparametric bilinear element enriched with one element-bubble on every triangle element or with two-element-bubbles on every quadrilateral element, respectively, is employed for each component of the nonsmooth solution. Due to the fact that the element-bubbles can be statically eliminated at element levels, our method is essentially three-nodes or four-nodes C (0) Lagrange element method. With two Fortin-type interpolations established, a very technical duality argument is elaborated to estimate the error for the indefinite problem. For the nonsmooth solution having the H (r) regularity where r may vary in the interval [0, 1), we obtain the error bound in an energy norm. Some numerical experiments are performed to confirm the theoretical error bounds.",
author = "Huoyuan Duan and Ping Lin and Tan, {Roger C. E.}",
year = "2012",
month = "9",
doi = "10.1007/s00211-012-0456-x",
volume = "122",
pages = "61--99",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer Verlag",
number = "1",
}