Summary
We propose hp-version interior penalty discontinuous Galerkin methods for the discretization of the curl-curl operator with divergence free constraint, often encountered in electromagnetic problems. For unstructured meshes with hanging nodes, we present error estimates that are optimal in the meshsize h and slightly suboptimal in the polynomial approximation order p. The performance of these methods is numerically tested for two-dimensional model problems.
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References
Alonso, A., Valli, A. (1997): A domain decomposition approach for heterogeneous timeharmonic Maxwell equations. Comput. Methods Appl. Mech. Engrg. 143, 97–112
Arnold, D.N., Brezzi, F., Cockburn, B., Marini, L.D. (2001): Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779
Cockburn, B., Karniadakis, G.E., Shu, C.-W. (2000): Discontinuous Galerkin methods. Theory, computation and applications. (Lecture Notes in Computer Science and Engineering, vol. 11). Springer, Berlin
Dauge, M., Costabel, M. (2002): Weighted regularization of Maxwell equations in polyhedral domains. Numer. Math. 93, 239–277
Georgoulis, E.H., Süli, E. (2001): hp-DGFEM on shape-irregular meshes: reactiondiffusion. Technical Report NA 01-09, Oxford University Computing Laboratory, Oxford
Houston, P., Schwab, C, Süli, E. (2002): Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39, 2133–2163
Perugia, I., Schötzau, D. (2002): An hp-analysis of the local discontinuous Galerkin method for diffusion problems. J. Sci. Comput. 17, 561–571
Perugia, I., Schötzau, D. (2001): The hp-ocal discontinuous Galerkin method for low-frequency time-harmonic Maxwell equations. Math. Comput., to appear. PII: S0025-5718(02)01471-0
Perugia, I., Schötzau, D., Monk, P. (2002): Stabilized interior penalty methods for the time-harmonic Maxwell equations. Comput. Methods Appl. Math. Engrg. 191, 4675–4697
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© 2003 Springer-Verlag Italia
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Houston, P., Perugia, I., Schötzau, D. (2003). hp-DGFEM for Maxwell’s equations. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds) Numerical Mathematics and Advanced Applications. Springer, Milano. https://doi.org/10.1007/978-88-470-2089-4_71
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DOI: https://doi.org/10.1007/978-88-470-2089-4_71
Publisher Name: Springer, Milano
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