Please use this identifier to cite or link to this item: https://doi.org/10.1137/050640102
Title: A least-squares finite element method for the magnetostatic problem in a multiply connected Lipschitz domain
Authors: Duan, H.-Y. 
Lin, P. 
Saikrishnan, P.
Tan, R.C.E. 
Keywords: Curl-div magnetostatic problem
L2 projector
Least-squares continuous finite element method
Issue Date: 2007
Citation: Duan, H.-Y., Lin, P., Saikrishnan, P., Tan, R.C.E. (2007). A least-squares finite element method for the magnetostatic problem in a multiply connected Lipschitz domain. SIAM Journal on Numerical Analysis 45 (6) : 2537-2563. ScholarBank@NUS Repository. https://doi.org/10.1137/050640102
Abstract: A new least-squares finite element method is developed for the curl-div magnetostatic problem in Lipschitz and multiply connected domains filled with anisotropic nonhomogeneous materials. In order to deal with possibly low regularity of the solution, local L2 projectors are introduced to standard least-squares formulation and applied to both curl and div operators. Coercivity is established by adding suitable mesh-dependent bilinear terms. As a result, any continuous finite elements (lower-order elements are enriched with suitable bubbles) can be employed. A desirable error bound is obtained: ∥u - uh∥0 ≤ C ∥u - ũ∥0, where uh and ũ are the finite element approximation and the finite element interpolant of the exact solution u, respectively. Numerical tests confirm the theoretical results. © 2007 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Numerical Analysis
URI: http://scholarbank.nus.edu.sg/handle/10635/102668
ISSN: 00361429
DOI: 10.1137/050640102
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