Divergence boundary conditions for vector Helmholtz equations with divergence constraints

Urve Kangro; Roy Nicolaides

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1999)

  • Volume: 33, Issue: 3, page 479-492
  • ISSN: 0764-583X

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Kangro, Urve, and Nicolaides, Roy. "Divergence boundary conditions for vector Helmholtz equations with divergence constraints." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 33.3 (1999): 479-492. <http://eudml.org/doc/193931>.

@article{Kangro1999,
author = {Kangro, Urve, Nicolaides, Roy},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {interior and boundary formulations of divergence constraints; finite elements; vector Helmholtz case of electromagnetics},
language = {eng},
number = {3},
pages = {479-492},
publisher = {Dunod},
title = {Divergence boundary conditions for vector Helmholtz equations with divergence constraints},
url = {http://eudml.org/doc/193931},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Kangro, Urve
AU - Nicolaides, Roy
TI - Divergence boundary conditions for vector Helmholtz equations with divergence constraints
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1999
PB - Dunod
VL - 33
IS - 3
SP - 479
EP - 492
LA - eng
KW - interior and boundary formulations of divergence constraints; finite elements; vector Helmholtz case of electromagnetics
UR - http://eudml.org/doc/193931
ER -

References

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  1. [1] M. Costabel, A Remark on the Regularity of Solutions of Maxwell's Equations on Lipschitz Domains. Math. Methods Appl. Sci. 12 (1990) 365-368. Zbl0699.35028MR1048563
  2. [2] V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer-Verlag (1986). Zbl0585.65077MR851383
  3. [3] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman Advanced Publishing Program (1985). Zbl0695.35060MR775683
  4. [4] C. Hazard and M. Lenoir, On the Solution of Time-harmonic Scattering Problems for Maxwell's Equations. SIAM J. Math. Anal 27 (1996) 1597-1630. Zbl0860.35129MR1416510
  5. [5] B.N. Jiang, J. Wu and L.A. Povinelli, The Origin of Spurious Solutions in Computational Electromagnetics. J. Comput. Phys. 125 (1995) 104-123. Zbl0848.65086MR1381806
  6. [6] M. Křížek and P. Neittaanmäki, On the Validity of Friedrichs' Inequalities. Math. Scand. 54 (1984), 17-26. Zbl0555.35003MR753060
  7. [7] I.D. Mayergoyz, A New Point of View on the Mathematical Structure of Maxwell's Equations. IEEE Trans. Magn. 29 (1993) 1315-1320. 
  8. [8] F. Murat, Compacité par Compensation. Ann. Scuola Norm. Sup.Pisa Cl. Sci. 5 (1978) 485-507. Zbl0399.46022MR506997

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