Exterior problem of the Darwin model and its numerical computation

Lung-an Ying; Fengyan Li

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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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Lung-an Ying, and Li, Fengyan. "Exterior problem of the Darwin model and its numerical computation ." ESAIM: Mathematical Modelling and Numerical Analysis 37.3 (2010): 515-532. <http://eudml.org/doc/194176>.

@article{Lung2010,
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 = {Lung-an Ying, Li, Fengyan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Darwin model; Maxwell's equations; exterior problem; infinite element method.; exterior problem; infinite element method},
language = {eng},
month = {3},
number = {3},
pages = {515-532},
publisher = {EDP Sciences},
title = {Exterior problem of the Darwin model and its numerical computation },
url = {http://eudml.org/doc/194176},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Lung-an Ying
AU - Li, Fengyan
TI - Exterior problem of the Darwin model and its numerical computation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
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.; exterior problem; infinite element method
UR - http://eudml.org/doc/194176
ER -

References

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  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. 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
  3. V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1988).  Zbl0396.65070
  4. V. Girault and A. Sequeira, A well-posed problem for the exterior stokes equations in two and three dimensions. Arch. Ration. Mech. Anal.114 (1991) 313–333.  Zbl0731.35078
  5. D.W. Hewett and C. Nielson, A multidimensional quasineutral plasma simulation model. J. Comput. Phys.29 (1978) 219–236.  Zbl0388.76108
  6. O.A. Ladyzhenskaya,The Mathematical Theory of Viscous Incompressible Flow. 2nd ed., Gordon and Breach, New York (1969).  Zbl0184.52603
  7. T.-T. Li and T. Qin, Physics and Partial Differential Equations. Higher Education Press, Beijing (1997).  
  8. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. 3rd ed., North-Holland (1984).  Zbl0568.35002
  9. L.-A. Ying, Infinite element approximation to axial symmetric Stokes flow. J. Comput. Math.4 (1986) 111–120.  Zbl0598.76034
  10. L.-A.Ying, Infinite Element Methods. Peking University Press, Beijing and Vieweg and Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden (1995).  

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