Finite element convergence for the Darwin model to Maxwell's equations

Ciarlet, Patrick; Zou, Jun

doi:10.1051/m2an/1997310202131

Cited by 38 publications

(42 citation statements)

References 15 publications

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“…This result follows from a theorem in [1]. Here we notice that the exact solution p = 0, so |p| 1(2) is bounded.…”

Section: Proof D(·mentioning

confidence: 60%

“…It was shown in [2] that the Darwin model approximates the Maxwell equations up to the second order for B and to the third order for E, provided η =v/c is small, wherev is a characteristic velocity. In [1] variational formulation and the finite element method for the Darwin model was studied. Two kinds of variational formulation were given.…”

Section: Introductionmentioning

confidence: 99%

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Exterior problem of the Darwin model and its numerical computation

Liu

2003

ESAIM: M2AN

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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.Mathematics Subject Classification. 35Q60, 65N30, 35J50.

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“…This result follows from a theorem in [1]. Here we notice that the exact solution p = 0, so |p| 1(2) is bounded.…”

Section: Proof D(·mentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Exterior problem of the Darwin model and its numerical computation

Liu

2003

ESAIM: M2AN

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“…If Ω represents exterior domains, C(t) is a constant independent of time t, for example C(t) = 1 if satisfying the boundary assumptions in [5].…”

Section: Maxwell's Equations and Darwin Modelmentioning

confidence: 99%

“…The details to discuss the variational formulations of Darwin model were given by P.Ciarlet,JR and J.Zou in [5]. They have studied the H(curl; Ω) and H(curl, div; Ω) variational formulations for Darwin model in three dimensions, and proved the well-posedness.…”

Section: Then There Exists a Unique Solution To The Saddle Point Probmentioning

confidence: 99%

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Darwin Approximation to Maxwell’s Equations

Fang

Liao

Ying

2009

Lecture Notes in Computer Science

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Abstract. Maxwell's equations are the foundation of electromagnetics, its extensive applications make computational electromagnetics a new rapidly growing subject. However, since the electric and the magnetic fields are coupling in the Maxwell system, the numerical solution of the full system of Maxwell's equations is extremely expensive in terms of computer time. Darwin model, which decouple the coupled system, is such a good approximation to Maxwell's equations. In three dimensional space case, it neglects the transverse component of the displacement current; while in two dimensional space case, Darwin model is equivalent to TE, TM models. For these reasons, it is worthwhile to investigate Darwin model, and a lot of works have been done to it. In this paper, we review the advance in the Darwin model and introduce some of our new results about the exterior problems of Darwin model and its numerical solutions with infinite elements methods.

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