Interior penalty discontinuous Galerkin method for Maxwell's equations: Energy norm error estimates

Journal of Computational and Applied Mathematics

Volumn 204, Issue 2 SPEC. ISS., 2007, Pages 375-386

  Grote, Marcus J ^a   Schneebeli, Anna ^a   Schötzau, Dominik ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

A priori error analysis; Discontinuous Galerkin methods; Maxwell equations

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MAXWELL EQUATIONS;

DISCONTINUOUS GALERKIN METHODS; LOW-REGULARITY SOLUTIONS; PRIORI ERROR ANALYSIS;

GALERKIN METHODS;

EID: 34247214527     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.01.044     Document Type: Article

References (28)

1. A. Buffa, I. Perugia, Discontinuous Galerkin approximation of the Maxwell eigenproblem, Technical Report PV-24, IMATI-CNR Pavia, 2005, Technical Report.
2. Cangellaris A.C., and Wright D.B. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antennas Propag. 39 (1991) 1518-1525
3. Chen M.-H., Cockburn B., and Reitich F. High-order RKDG methods for computational electromagnetics. J. Sci. Comput. 22 (2005) 205-226
4. E.T. Chung, B. Engquist, Optimal discontinuous Galerkin methods for wave propagation, preprint.
5. Ciarlet P.G. The Finite Element Method for Elliptic Problems (1978), North-Holland, Amsterdam
6. Cockburn B., Li F., and Shu C.-W. Locally divergence-free discontinuous Galerkin methods for the Maxwell equations. J. Comput. Phys. 194 (2004) 588-610
7. Cockburn B., and Shu C.-W. TVB Runge-Kutta local projection discontinuous Galerkin method for conservation laws II: General framework. Math. Comput. 52 186 (1989) 411-435
8. Elmkies A., and Joly P. Finite elements and mass lumping for Maxwell's equations: the 2d case. Numerical Analysis, C.R. Acad. Sci. Paris 324 (1997) 1287-1293
9. Fezoui L., Lanteri S., Lohrengel S., and Piperno S. Convergence and stability of a discontinuous Galerkin time-domain methods for the 3D heterogeneous Maxwell equations on unstructured meshes. Modél. Math. Anal. Numér. 39 6 (2005) 1149-1176
10. M.J. Grote, A. Schneebeli, D. Schötzau, Discontinuous Galerkin finite element method for the wave equation, Technical Report 3, Mathematisches Institut, Universität Basel, 2005, SIAM J. Numer. Anal., in press.
11. Hesthaven J.S., and Warburton T. Nodal high-order methods on unstructured grids. I. Time-domain solution of Maxwell's equations. J. Comput. Phys. 181 (2002) 186-221
12. Houston P., Perugia I., Schneebeli A., and Schötzau D. Interior penalty method for the indefinite time-harmonic Maxwell equations. Numer. Math. 100 (2005) 485-518
13. Houston P., Perugia I., and Schötzau D. Mixed discontinuous Galerkin approximation of the Maxwell operator. SIAM J. Numer. Anal. 42 (2004) 434-459
14. Jiang B., Wu J., and Povinelli L.A. The origin of spurious solutions in computational electromagnetics. J. Comput. Phys. 125 (1996) 104
15. D. Kopriva, S.L. Woodruff, M.Y. Hussaini, Discontinuous spectral element approximation of Maxwell's equations, in: B. Cockburn, G.E. Karniadakis, C.-W. Shu (Eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Lecture Notes in Computer Science Engineering, vol. 11, Springer, Berlin, 2000, pp. 355-362.
16. Lee R.L., and Madsen N.K. A mixed finite element formulation for Maxwell's equations in the time domain. J. Comput. Phys. 88 (1990) 284-304
17. Monk P. A comparison of three mixed methods for the time-dependent Maxwell's equations. SIAM J. Sci. Statist. Comput. 13 (1992) 1097-1122
18. Monk P. Finite Element Methods for Maxwell's Equations (2003), Oxford University Press, New York
19. 3. Numer. Math. 35 (1980) 315-341
20. 3. Numer. Math. 50 (1986) 57-81
21. Paulsen K.D., and Lynch D.R. Elimination of vector parasities in finite element Maxwell solutions. IEEE Trans. Microwave Theory Tech. 39 (1991) 395-404
22. Perugia I., and Schötzau D. An hp-analysis of the local discontinuous Galerkin method for diffusion problems. J. Sci. Comput. 17 (2002) 561-571
23. B. Rivière, M.F. Wheeler, Discontinuous finite element methods for acoustic and elastic wave problems, I: Semidiscrete error estimates, Technical Report 01-02, TICAM, UT, Austin, 2001.
24. Rivière B., and Wheeler M.F. Discontinuous finite element methods for acoustic and elastic wave problems. ICM2002-Beijing Satellite Conference on Scientific Computing, Contemporary Mathematics vol. 329 (2003), American Mathematical Society, Providence, RI 271-282
25. Taflove A. Computational Electrodynamics: The Finite-Difference Time-Domain Method (1995), Artech House, Boston
26. T. Warburton, Application of the discontinuous Galerkin method to Maxwell's equations using unstructured polymorphic hp-finite elements, in: B. Cockburn, G.E. Karniadakis, C.-W. Shu, (Eds.), Discontinuous Galerkin Methods: Theory, Computation and Applications, Lecture Notes in Computer Science Engineering, vol. 11, Springer, Berlin, 2000, pp. 451-458.
27. Warburton T., and Embree M. The role of the penalty in the local discontinuous Galerkin method for Maxwell's eigenvalue problem. Comput. Methods Appl. Mech. Eng. 195 (2006) 3205-3223
28. Yee K.S. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Trans. Antennas Propag. 14 (1966) 302-307