, Volume 55, Issue 3, pp 738-754

An Adaptive P 1 Finite Element Method for Two-Dimensional Maxwell’s Equations

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Abstract

Recently a new numerical approach for two-dimensional Maxwell’s equations based on the Hodge decomposition for divergence-free vector fields was introduced by Brenner et al. In this paper we present an adaptive P 1 finite element method for two-dimensional Maxwell’s equations that is based on this new approach. The reliability and efficiency of a posteriori error estimators based on the residual and the dual weighted-residual are verified numerically. The performance of the new approach is shown to be competitive with the lowest order edge element of Nédélec’s first family.

This work was supported in part by the National Science Foundation under Grant No. DMS-07-13835 and Grand No. DMS-10-16332. The second author was additionally supported by the DFG Research Center MATHEON “Mathematics for Key Technologies” and the DFG graduate school BMS “Berlin Mathematical School”.