Journal article
Numerical solution of an H(curl)-elliptic hemivariational inequality
IMA journal of numerical analysis, Vol.43(2), pp.976-1000
03/2023
DOI: 10.1093/imanum/drac007
Abstract
This paper is concerned with the analysis and numerical solution of an H(curl)-elliptic hemivariational inequality (HVI). One source of the HVI is through a temporal semidiscretization of a related hyperbolic Maxwell equation problem. An equivalent minimization principle is introduced, and the solution existence and uniqueness of the H(curl)-elliptic HVI are proved. Numerical analysis of the HVI is provided with a general Galerkin approximation, including a Cea's inequality for convergence and error estimation. When the linear edge finite element method is employed, an optimal-order error estimate is derived under a suitable solution regularity assumption. A fully discrete scheme based on the backward Euler difference in time and a mixed finite element method in space is also analyzed, and stability estimates are derived for first-order terms of the fully discrete solution. Numerical results are reported on linear edge finite element solutions of the H(curl)-elliptic HVI for numerical evidence of the theoretically predicted convergence order.
Details
- Title: Subtitle
- Numerical solution of an H(curl)-elliptic hemivariational inequality
- Creators
- Weimin Han - Univ Iowa, Dept Math, Iowa City, IA 52242 USAMin Ling - Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R ChinaFei Wang - Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
- Resource Type
- Journal article
- Publication Details
- IMA journal of numerical analysis, Vol.43(2), pp.976-1000
- Publisher
- Oxford Univ Press
- DOI
- 10.1093/imanum/drac007
- ISSN
- 0272-4979
- eISSN
- 1464-3642
- Number of pages
- 25
- Grant note
- 12171383 / National Natural Science Foundation of China; National Natural Science Foundation of China (NSFC) 850737 / Simons Foundation Collaboration
- Language
- English
- Electronic publication date
- 03/18/2022
- Date published
- 03/2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984242350602771
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