Article

Journal of Scientific Computing

, Volume 55, Issue 3, pp 738-754

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

  • S. C. BrennerAffiliated withDepartment of Mathematics and Center for Computation & Technology, Louisiana State University Email author 
  • , J. GedickeAffiliated withInstitut für Mathematik, Humboldt-Universität zu Berlin
  • , L.-Y. SungAffiliated withDepartment of Mathematics and Center for Computation & Technology, Louisiana State University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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