Exterior problem of the Darwin model and its numerical computation

Lung-An Ying; Fengyan Li

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 3, page 515-532
  • ISSN: 0764-583X

Abstract

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In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.

How to cite

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Ying, Lung-An, and Li, Fengyan. "Exterior problem of the Darwin model and its numerical computation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.3 (2003): 515-532. <http://eudml.org/doc/245759>.

@article{Ying2003,
abstract = {In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.},
author = {Ying, Lung-An, Li, Fengyan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Darwin model; Maxwell’s equations; exterior problem; infinite element method; Maxwell's equations},
language = {eng},
number = {3},
pages = {515-532},
publisher = {EDP-Sciences},
title = {Exterior problem of the Darwin model and its numerical computation},
url = {http://eudml.org/doc/245759},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Ying, Lung-An
AU - Li, Fengyan
TI - Exterior problem of the Darwin model and its numerical computation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 3
SP - 515
EP - 532
AB - In this paper, we study the exterior boundary value problems of the Darwin model to the Maxwell’s equations. The variational formulation is established and the existence and uniqueness is proved. We use the infinite element method to solve the problem, only a small amount of computational work is needed. Numerical examples are given as well as a proof of convergence.
LA - eng
KW - Darwin model; Maxwell’s equations; exterior problem; infinite element method; Maxwell's equations
UR - http://eudml.org/doc/245759
ER -

References

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  1. [1] P. Ciarlet Jr and J. Zou, Finite element convergence for the Darwin model to Maxwell’s equations. Math. Modelling Numer. Anal. 31 (1997) 213–250. Zbl0887.65121
  2. [2] P. Degond and P.A. Raviart, An analysis of the Darwin model of approximation to Maxwell’s equations. Forum Math. 4 (1992) 13–44. Zbl0755.35137
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  7. [7] T.-T. Li and T. Qin, Physics and Partial Differential Equations. Higher Education Press, Beijing (1997). 
  8. [8] R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. 3rd ed., North-Holland (1984). Zbl0568.35002MR769654
  9. [9] L.-A. Ying, Infinite element approximation to axial symmetric Stokes flow. J. Comput. Math. 4 (1986) 111–120. Zbl0598.76034
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