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Exterior problem of the Darwin model and its numerical computation

Published online by Cambridge University Press:  15 April 2004

Lung-an Ying  and
Fengyan Li
Lung-an Ying
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, PR China. [email protected].
Fengyan Li
Affiliation:
School of Mathematical Sciences, Peking University, PR China. Division of Applied Math., Brown University, RI 02912, USA. [email protected].
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Abstract

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

Keywords

Darwin modelMaxwell's equationsexteriorprobleminfinite element method.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 3 , May 2003 , pp. 515 - 532
Copyright
© EDP Sciences, SMAI, 2003

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References

Ciarlet Jr, P. and Zou, J., Finite element convergence for the Darwin model to Maxwell's equations. Math. Modelling Numer. Anal. 31 (1997) 213–250. CrossRef
Degond, P. and Raviart, P.A., An analysis of the Darwin model of approximation to Maxwell's equations. Forum Math. 4 (1992) 13–44. CrossRef
V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations. Springer, Berlin (1988).
Girault, V. and Sequeira, A., A well-posed problem for the exterior stokes equations in two and three dimensions. Arch. Ration. Mech. Anal. 114 (1991) 313–333. CrossRef
Hewett, D.W. and Nielson, C., A multidimensional quasineutral plasma simulation model. J. Comput. Phys. 29 (1978) 219–236. CrossRef
O.A. Ladyzhenskaya,The Mathematical Theory of Viscous Incompressible Flow. 2nd ed., Gordon and Breach, New York (1969).
T.-T. Li and T. Qin, Physics and Partial Differential Equations. Higher Education Press, Beijing (1997).
R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis. 3rd ed., North-Holland (1984).
Ying, L.-A., Infinite element approximation to axial symmetric Stokes flow. J. Comput. Math. 4 (1986) 111–120.
L.-A.Ying, Infinite Element Methods. Peking University Press, Beijing and Vieweg and Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden (1995).