Locally divergence-free discontinuous Galerkin methods for the Maxwell equations

Journal of Computational Physics

Volumn 194, Issue 2, 2004, Pages 588-610

  Cockburn, Bernardo ^a   Li, Fengyan ^b   Shu, Chi Wang ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Divergence free; Maxwell equations

Indexed keywords

GALERKIN METHODS; POLYNOMIALS;

APPROXIMATE SOLUTION; COMPUTATIONAL COSTS; DISCONTINOUS GALERKIN METHODS; DIVERGENCE FREE; LOCALLY DIVERGENCE-FREE; ORDER OF ACCURACY; PIECEWISE POLYNOMIALS; POLYNOMIAL BASIS; POLYNOMIAL SPACE; POST-PROCESSING TECHNIQUES;

MAXWELL EQUATIONS;

EID: 1442306605     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.09.007     Document Type: Article

References (22)

1. F. Assous, P. Degond, E. Heintze, P.A. Raviart, J. Segre, On a finite element method for solving the three dimensional Maxwell equations, Journal of Computational Physics 109 (1993) 222-237.
2. G.A. Baker, W.N. Jureidini, O.A. Karakashian, Piecewise solenoidal vector fields and the Stokes problem, SIAM Journal on Numerical Analysis 27 (1990) 1466-1485.
3. D.S. Balsara, D.S. Spicer, A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations, Journal of Computational Physics 149 (1999) 270-292.
4. J. Bramble, T. Sun, A negative-norm least squares method for Reissner-Mindlin plates, Mathematics of Computation 67 (1998) 901-916.
5. F. Brezzi, J. Douglas Jr., L.D. Marini, Two families of mixed finite elements for second order elliptic problems, Numerische Mathematik 47 (1985) 217-235.
6. P. Ciarlet, The Finite Element Methods for Elliptic Problems, North-Holland, Amsterdam, 1975.
7. B. Cockburn, Discontinuous Galerkin methods for convection-dominated problems, in: T.J. Barth, H. Deconinck (Eds.), High-Order Methods for Computational Physics, Lecture Notes in Computational Science and Engineering, vol. 9, Springer, Berlin, 1999, pp. 69-224.
8. B. Cockburn, S. Hou, C.-W. Shu, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case, Mathematics of Computation 54 (1990) 545-581.
9. B. Cockburn, G. Karniadakis, C.-W. Shu, The development of discontinuous Galerkin methods, in: B Cockburn, G. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Lecture Notes in Computational Science and Engineering, vol. 11, Springer, Berlin, 2000, pp. 3-50, Part I: Overview.
10. B. Cockburn, M. Luskin, C.-W. Shu, E. Süli, Enhanced accuracy by post-processing for finite element methods for hyperbolic equations, Mathematics of Computation 72 (2003) 577-606.
11. B. Cockburn, C.-W. Shu, The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems, Journal of Computational Physics 141 (1998) 199-224.
12. B. Cockburn, C.-W. Shu, The local discontinuous Galerkin method for time-dependent convection-diffusion systems, SIAM Journal on Numerical Analysis 35 (1998) 2440-2463.
13. B. Cockburn, C.-W. Shu, Runge-Kutta Discontinuous Galerkin methods for convection-dominated problems, Journal of Scientific Computing 16 (2001) 173-261.
14. S. Gottlieb, C.-W. Shu, E. Tadmor, Strong stability preserving high order time discretization methods, SIAM Review 43 (2001) 89-112.
15. J.S. Hesthaven, T. Warburton, Nodal high-order methods on unstructured grids. I. time-domain solution of Maxwell's equations, Journal of Computational Physics 181 (2002) 186-221.
16. B.-N. Jiang, J. Wu, L.A. Povinelli, The origin of spurious solutions in computational electromagnetics, Journal of Computational Physics 125 (1996) 104-123.
17. G.-S. Jiang, C.-W. Shu, On cell entropy inequality for discontinuous Galerkin methods, Mathematics of Computation 62 (1994) 531-538.
18. O.A. Karakashian, W.N. Jureidini, A nonconforming finite element method for the stationary Navier-Stokes equations, SIAM Journal on Numerical Analysis 35 (1998) 93-120.
19. C.-D. Munz, P. Omnes, R. Schneider, E. Sonnendrücker, U. Voß, Divergence correction techniques for Maxwell solvers based on a hyperbolic model, Journal of Computational Physics 161 (2000) 484-511.
20. R.A. Nicolaides, D.-Q. Wang, Convergence analysis of a covolume scheme for Maxwell's equations in three dimensions, Mathematics of Computation 67 (1998) 947-963.
21. J. Ryan, C.-W. Shu, H. Atkins, Extension of a post-processing technique for the discontinuous Galerkin method for hyperbolic equations with application to an aeroacoustic problem, SIAM Journal on Scientific Computing (submitted).
22. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Transactions on Antenna Propagation AP 14 (1966) 302-307.