Mixed discontinuous Galerkin approximation of the maxwell operator: Non-stabilized formulation

Journal of Scientific Computing

Volumn 22-23, Issue , 2005, Pages 315-346

  Houston, Paul ^a   Perugia, Ilaria ^b   Schötzau, Dominik ^c  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b UNIVERSITY OF PAVIA   (Italy)

^c UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Discontinuous Galerkin methods; Maxwell operator; Mixed methods

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS;

DISCONTINUOUS GALERKIN METHOD; MAXWELL METHOD; MIXED METHODS; SPACE DIMENSIONS;

GALERKIN METHODS;

EID: 17444426685     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10915-004-4142-8     Document Type: Article

References (17)

1. Alonso, A., and Valli, A. (1999). An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations. Math. Comput. 68, 607-631.
2. Arnold, D. N., Brezzi, F., Cockburn, B., and Marini, L. D. (2001). Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749-1779.
3. Brezzi, F., and Fortin, M. (1991). Mixed and hybrid finite element methods. In Springer Series in Computational Mathematics, Vol. 15, Springer-Verlag, New York.
4. Brezzi, F., and Fortin, M. (2001). A minimal stabilisation procedure for mixed finite element methods. Numer. Math. 89, 457-491.
5. Demkowicz, L., and Vardapetyan, L. (1998). Modeling of electromagnetic absorption/scattering problems using hp-adaptive finite elements. Comput. Meth. Appl. Mech. Eng. 152, 103-124.
6. Hiptmair, R. (2002). Finite elements in computational electromagnetism. Acta Numer. 11, 237-339.
7. Houston, P., Perugia, I., and Schötzau, D. (2004). Mixed discontinuous Galerkin approximation of the Maxwell operator. SIAM J. Numer. Anal. 42, 434-459.
8. Houston, P., Perugia, I., and Schötzau, D. (2003). hp-DGFEM for Maxwell's equations. In Brezzi, F., Buffa, A., Corsaro, S., and Murli, A. (eds.), Numerical Mathematics and Advanced Applications ENUMATH 2001, Springer-Verlag, New york, pp. 785-794.
9. Houston, P., Perugia, I., and Schötzau, D. (2004). Nonconforming Mixed Finite Element Approximations to Time-Harmonic Eddy Current Problems. Technical Report 2003/15, University of Leicester, Department of Mathematics. IEEE Trans. Mag. 40, 1268-1273.
10. Karakashian, O. A., and Pascal, F. (2003). A posteriori error estimation for a discontinuous Galerkin approximation of second order elliptic problems. SIAM J. Numer. Anal. 41, 2374-2399.
11. Monk, P. (2003). Finite Element Methods for Maxwell's Equations, Oxford University Press, Oxford.
12. 3. Numer. Math. 35, 315-341.
13. 3. Numer. Math. 39, 97-112.
14. 3. Numer. Math. 50, 57-81.
15. p-local discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations. Math. Comput. 72, 1179-1214.
16. Perugia, I., Schötzau, D., and Monk, P. (2002). Stabilized interior penalty methods for the time-harmonic Maxwell equations. Comput. Meth. Appl. Mech. Eng. 191, 4675-4697.
17. p-adaptive finite elements in electromagnetics. Comput. Meth. Appl. Mech. Eng. 169, 331-344.