**C-0 elements for generalized indefinite Maxwell equations.** / Duan, Huoyuan; Lin, Ping; Tan, Roger C. E.

Research output: Contribution to journal › Article

Duan, H, Lin, P & Tan, RCE 2012, 'C-0 elements for generalized indefinite Maxwell equations' *Numerische Mathematik*, vol 122, no. 1, pp. 61-99., 10.1007/s00211-012-0456-x

Duan, H., Lin, P., & Tan, R. C. E. (2012). C-0 elements for generalized indefinite Maxwell equations. *Numerische Mathematik*, *122*(1), 61-99. 10.1007/s00211-012-0456-x

Duan H, Lin P, Tan RCE. C-0 elements for generalized indefinite Maxwell equations. Numerische Mathematik. 2012 Sep;122(1):61-99. Available from: 10.1007/s00211-012-0456-x

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title = "C-0 elements for generalized indefinite Maxwell equations",

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",

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TY - JOUR

T1 - C-0 elements for generalized indefinite Maxwell equations

AU - Duan,Huoyuan

AU - Lin,Ping

AU - Tan,Roger C. E.

PY - 2012/9

Y1 - 2012/9

N2 - <p>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.</p>

AB - <p>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.</p>

U2 - 10.1007/s00211-012-0456-x

DO - 10.1007/s00211-012-0456-x

M3 - Article

VL - 122

SP - 61

EP - 99

JO - Numerische Mathematik

T2 - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 1

ER -