Abstract
In this paper, we study the TE, TM model by using the decompositions of the vector fields in 2-D bounded multiply connected domains and 2-D unbounded domains, respectively. We find that the TE, TM model and the Darwin models are equivalent if we assume some regularity of the initial data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ciarlet P, Zou J. Finite element convergence for the Darwin model to Maxwell’s equations. RAIRO Math Model Numer Anal, 1997, 31: 213–249
Degond P, Raviart P A. An analysis of the Darwin model of approximation to Maxwell’s equations. Forum Math, 1992, 4: 13–44
Girault V, Raviart P A. Finite Element Methods for Navier-Stokes Equations. Berlin: Springer, 1988
Ladyzhenskaya O A. The Mathematical Theory of Viscous Incompressible Flow, 2nd ed. New York: Gordon and Breach, 1969
Liao C X, Ying L A. Exterior problem of magnetic field in Darwin model and its numerical solution. Numer Methods Partial Differential Equations, 2008, 24: 418–434
Taylor A E, Lay D C. Introduction to Functional Analysis. New York: John Wiley, 1980
Ying L A. Numerical Methods for Exterior Problems. Singapore: World Scientific, 2006
Ying L A, Li F Y. Exterior problem of the Darwin model and its numerical computation. Math Model Numer Anal, 2003, 37: 515–532
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liao, C., Ying, L. The equivalence between the TE, TM model and the Darwin models. Sci. China Math. 53, 993–1010 (2010). https://doi.org/10.1007/s11425-009-0185-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-009-0185-5