A discontinuous Galerkin method for 3D Maxwell’s equation on non-conforming grids. (English) Zbl 1075.78002

Cohen, Gary C. (ed.) et al., Mathematical and numerical aspects of wave propagation, WAVES 2003. Proceedings of the sixth international conference on mathematical and numerical aspects of wave propagation, Jyväskylä, Finland, 30 June – 4 July 2003. Berlin: Springer (ISBN 3-540-40127-X/hbk). 389-394 (2003).
For 3D Maxwell’s system the authors propose an explicit scheme based on the discontinuous Galerkin method introduced in [P. Lasaint and P. A. Raviart, On a finite element method for solving the neutron transport equation, Mathematical Aspect of Finite Element in Partial Differential Equations, Madison 1974, 89–123 (1974; Zbl 0341.65076)], non-conforming grids. It is proved that this scheme is stable, converses a discrete energy and is able to work on level refined grids without any noticeable dispersion effect even for long time computations.
For the entire collection see [Zbl 1029.00072].


78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs


Zbl 0341.65076