Journal of Scientific Computing

, Volume 55, Issue 3, pp 738–754

# An Adaptive P1 Finite Element Method for Two-Dimensional Maxwell’s Equations

• S. C. Brenner
• J. Gedicke
• L.-Y. Sung
Article

## 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.

## Keywords

Adaptivity Error estimators Finite element method Hodge decomposition Maxwell’s equations

## Notes

### Acknowledgements

The bulk of this paper was written while the second author enjoyed the hospitality of the Center for Computation and Technology at Louisiana State University.

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