A polynomial-degree-robust a posteriori error estimator for Nédélec discretizations of magnetostatic problems

英文摘要：

We present an equilibration-based a posteriori error estimator for Nédélec element discretizations of the magnetostatic problem. The estimator is obtained by adding a gradient correction to the estimator for Nédélec elements of arbitrary degree presented in [J. Gedicke, S. Geevers, and I. Perugia. An equilibrated a posteriori error estimator for arbitrary-order Nédélec elements for magnetostatic problems. Journal of Scientific Computing, 83:1-23, 2020]. This new estimator is proven to be reliable, with reliability constant 1, and efficient, with an efficiency constant that is independent of the polynomial degree of the approximation. These properties are demonstrated in a series of numerical experiments on three-dimensional test problems.