A Convergent adaptive edge element method for an optimal control problem in magnetostatics

Xu, Yifeng; Zou, Jun

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 2, pp. 615-640.

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.

Classification : 65N12, 65N15, 65N30, 35Q60, 49K20, 49M05
Mots clés : Optimal control, magnetostatic Maxwell equation, a posteriori error estimate, edge element, adaptive convergence

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