Please use this identifier to cite or link to this item: https://doi.org/10.1137/110850578
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dc.titleA delta-regularization finite element method for a double curl problem with divergence-free constraint
dc.contributor.authorDuan, H.
dc.contributor.authorLi, S.
dc.contributor.authorTan, R.C.E.
dc.contributor.authorZheng, W.
dc.date.accessioned2014-10-28T02:27:54Z
dc.date.available2014-10-28T02:27:54Z
dc.date.issued2012
dc.identifier.citationDuan, H., Li, S., Tan, R.C.E., Zheng, W. (2012). A delta-regularization finite element method for a double curl problem with divergence-free constraint. SIAM Journal on Numerical Analysis 50 (6) : 3208-3230. ScholarBank@NUS Repository. https://doi.org/10.1137/110850578
dc.identifier.issn00361429
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/102633
dc.description.abstractTo deal with the divergence-free constraint in a double curl problem, curl μ-1curl u = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method, curl μ-1curl uδ + δεuδ = f, to completely ignore the divergence-free constraint div εu = 0. We show that uδ converges to u in H(curl ; Ω) norm as δ → 0. The edge finite element method is then analyzed for solving uδ. With the finite element solution uδ,h, a quasioptimal error bound in the H(curl ;Ω) norm is obtained between u and uδ,h, including a uniform (with respect to δ) stability of uδ,h in the H(curl ; Ω) norm. All the theoretical analysis is done in a general setting, where μ and ε may be discontinuous, anisotropic, and inhomogeneous, and the solution may have a very low piecewise regularity on each material subdomain Ωj with u, curl u € (Hr(Ωj ))3 for some 0 < r < 1, where r may not be greater than 1/2. To establish the uniform stability and the error bound for r ≤ 1/2, we have respectively developed a new theory for the Kh ellipticity (related to mixed methods) and a new theory for the Fortin interpolation operator. Numerical results confirm the theory. © 2012 Society for Industrial and Applied Mathematics.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1137/110850578
dc.sourceScopus
dc.subjectDivergence-free constraint
dc.subjectDouble curl problem
dc.subjectEdge element
dc.subjectError bound
dc.subjectFortin operator
dc.subjectKh ellipticity
dc.subjectRegularization
dc.subjectUniform stability
dc.typeArticle
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1137/110850578
dc.description.sourcetitleSIAM Journal on Numerical Analysis
dc.description.volume50
dc.description.issue6
dc.description.page3208-3230
dc.description.codenSJNAA
dc.identifier.isiut000312733000018
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