Journal of Scientific Computing

, Volume 67, Issue 2, pp 453–474 | Cite as

Computational Performance of LDG Methods Applied to Time Harmonic Maxwell Equation in Polyhedral Domains



A numerical study of the classical and penalized LDG method applied to vector Helmholtz equation on three dimensional domains is presented. Using a simple numerical flux based on convex combinations classical rates of convergence can be obtained on unstructured meshes while achieving a substantial reduction of the stencil. The superconvergent behaviour of the auxiliary field is investigated on Cartesian meshes. Numerical experiments also suggest convergence of the method for constant approximations on Cartesian meshes. We explore existing scalable preconditioning techniques adapted to the discontinuous Galerkin framework for the low frequency case. Finally the method is tested on examples arising in practical engineering problems with complex valued electric field.


Local discontinuous Galerkin method Discontinuous Galerkin methods High order finite element Time harmonic Maxwell equation Vector Helmholtz equation 

Mathematics Subject Classification

65M60 65M08 65-05 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of Puerto RicoMayagüezUSA

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