Time-discrete finite element schemes for Maxwell's equations

Ch. G. Makridakis; P. Monk

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1995)

  • Volume: 29, Issue: 2, page 171-197
  • ISSN: 0764-583X

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Makridakis, Ch. G., and Monk, P.. "Time-discrete finite element schemes for Maxwell's equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 29.2 (1995): 171-197. <http://eudml.org/doc/193771>.

@article{Makridakis1995,
author = {Makridakis, Ch. G., Monk, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {time-discrete finite element schemes; Maxwell's equations; rational Padé approximations; error estimates},
language = {eng},
number = {2},
pages = {171-197},
publisher = {Dunod},
title = {Time-discrete finite element schemes for Maxwell's equations},
url = {http://eudml.org/doc/193771},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Makridakis, Ch. G.
AU - Monk, P.
TI - Time-discrete finite element schemes for Maxwell's equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1995
PB - Dunod
VL - 29
IS - 2
SP - 171
EP - 197
LA - eng
KW - time-discrete finite element schemes; Maxwell's equations; rational Padé approximations; error estimates
UR - http://eudml.org/doc/193771
ER -

References

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  2. [2] G. BAKER and J. BRAMBLE, 1979, Semidiscrete and single step fully discrete approximations for second order hyperbolic equations, RAIRO Anal. Numer, 13, 75-100. Zbl0405.65057MR533876
  3. [3] A. BOSSAVIT, 1990, Solving Maxwell equations in a closed cavity, and the question of « spurious » modes, IEEE Trans. Mag., 26, 702-705. 
  4. [4] P. CIARLET, 1978, The Finite Element Method for Elliptic Problems, vol. 4 of Studies in Mathematics and It's Applications, Elsevier North-Holland, NewYork. Zbl0383.65058MR520174
  5. [5] F. DUBOIS, 1990, Discrete vector potential representation of a divergence free vector field in three dimensional domains : numerical analysis of a model problem, SIAM J. Numer. Anal., 27, 1103-1142. Zbl0717.65086MR1061122
  6. [6] V. GlRAULT, 1988, Incompressible finite element methods for Navier-Stokes equations with nonstandard boundary conditions in R3, Math. Comp., 51,53-58. Zbl0666.76053
  7. [7] V. GIRAULT, 1990, Curl-conforming finite element methods for Navier-Stokes equations with non-standard boundary conditions in R3, in The Navier-Stokes equations. Theory and Numerical Methods, Lecture Notes, 1431,Springer, 201-218. Zbl0702.76037MR1072191
  8. [8] V. GIRAULT and P. RAVIART, 1986, Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, New York. Zbl0585.65077MR851383
  9. [9] M. KŘÍŽEK and P. NEITTAANMÄKI, 1989, On time-harmonic Maxwell equations with nonhomogeneous conductivities : solvability and FE-approximation, Aplikace Matematiky, 34, 480-499. Zbl0696.65085MR1026513
  10. [10] R. LEIS, 1988, Initial Boundary Value Problems in Mathematical Physics, John Wiley, New York. Zbl0599.35001
  11. [11] K. MAHADEVAN and R. MITTRA, 1993, Radar cross section computations of inhomogeneous scatterers using edge-based finite element method in frequency and time domains, Radio Science, 28, 1181-1193. 
  12. [12] K. MAHADEVAN, R. MITTRA and P. M. VAIDYA, 1993, Use of Whitney's edge and face elements for efficient finite element time domain solution of Maxwell's equation, Preprint. 
  13. [13] C. G. MAKRIDAKIS, 1992, On mixed finite element methods in linear elastodynamics, Numer. Math., 61, 235-260. Zbl0734.73074MR1147578
  14. [14] P. MONK, 1993, An analysis of Nédélec's method for the spatial discretization of Maxwell's equations, J. Comp. Appl. Math., 47, 101-121. 3 Zbl0784.65091MR1226366
  15. [15] J. NÉDÉLEC, 1980, Mixed finite elements in R3, Numer. Math., 35, 315-341. Zbl0419.65069MR592160
  16. [16] J. NÉDÉLEC, Éléments finis mixtes incompressibles pour l'équation de Stokes dans R3, Numer. Math., 39, 97-112. Zbl0488.76038
  17. [17] K. YEE, 1966, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. on Antennas and Propagation, AP-16, 302-307. Zbl1155.78304

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