1 Department of Mathematics, Scientific Computing Key Laboratory of Shanghai Universities and E-Institute for Computational Science of Shanghai Universities, Shanghai Normal University, Shanghai 200234, P.R. China.
2 Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, P.R. China.
Received: 3 December 2014
Revised: 7 February 2016
Accepted: 21 April 2016
This work is concerned with an adaptive edge element solution of an optimal control problem associated with a magnetostatic saddle-point Maxwell’s system. An a posteriori error estimator of the residue type is derived for the lowest-order edge element approximation of the problem and proved to be both reliable and efficient. With the estimator and a general marking strategy, we propose an adaptive edge element method, which is demonstrated to generate a sequence of discrete solutions converging strongly to the exact solution satisfying the resulting optimality conditions and guarantee a vanishing limit of the error estimator.
Mathematics Subject Classification: 65N12 / 65N15 / 65N30 / 35Q60 / 49K20 / 49M05
Key words: Optimal control / magnetostatic Maxwell equation / a posteriori error estimate / edge element / adaptive convergence
The research of Yifeng Xu was in part supported by NSFC (11201307), MOE of China through Specialized Research Fund for the Doctoral Program of Higher Education (20123127120001), E-Institute of Shanghai Universities (E03004) and Innovation Program of Shanghai Municipal Education Commission (13YZ059). The major part of the work was completed when the author visited The Chinese University of Hong Kong under the support of a Direct Grant for Research from CUHK.
© EDP Sciences, SMAI 2017