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A comparison of three mixed methods for the time-dependent Maxwell’s equations. (English) Zbl 0762.65081
The dispersions properties of the Lee-Madsen method are investigated analytically. The corresponding algorithm of R. L. Lee and N. K. Madsen [J. Comput. Phys. 88, No. 2, 284-304 (1990; Zbl 0703.65082)] is compared with two other mixed finite element methods due (in three dimensions) to J.-C. Nédélec [Numer. Math. 35, 315-341 (1980; Zbl 0419.65069)] and to the author [A mixed method for approximating Maxwell’s equations, J. Comput. Appl. Math. (to appear)].
The connection between the mixed finite element methods analyzed here and the standard finite difference method for Maxwell’s equations, developed by K. Yee [Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Ann. Prop. AP–16, 302-307 (1966)] is also shown.

MSC:
65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A25 Electromagnetic theory, general
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