A regularization method for stationary maxwell equations in an inhomogeneous conducting medium

Kremer, I. A.; Urev, M. V.

doi:10.1134/s1995423909020049

Cited by 2 publications

(3 citation statements)

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“…It was also shown in [4] that, for any positive value of the regularization parameter, the resulting regularized problem is equivalent to the original one.…”

Section: Introductionmentioning

confidence: 94%

“…The bilinear form is elliptic and continuous on (see [ Our goal is to estimate the error in the norm, which is equivalent to the norm generated by the bilinear form (see [4]). For this purpose, we first estimate for and then apply the triangle inequality and inequality (2.4) for .…”

Section: Statement Of the Generalized Regularized Problemmentioning

confidence: 99%

“…In [4] the generalized formulation of problem (0.5) was reduced, by eliminating the Lagrange multi plier, to a regularized form for the single one unknown vector function without the restricting diver gence condition. It was also shown in [4] that, for any positive value of the regularization parameter, the resulting regularized problem is equivalent to the original one.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Regularization method for solving the quasi-stationary Maxwell equations in an inhomogeneous conducting medium

Ivanov¹,

Kremer²,

Urev

2012

Comput. Math. and Math. Phys.

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Nedelec vector finite elements are used for the numerical solution of a regularized version of the quasi stationary Maxwell equations written in terms of a scalar and a vector magnetic potential with special calibration taking into account the conductivity of the medium. An optimal energy esti mate for the error of the approximate solution in Lipschitz polyhedral domains is established. Numer ical results are presented that demonstrate the stability of the method.

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“…It was also shown in [4] that, for any positive value of the regularization parameter, the resulting regularized problem is equivalent to the original one.…”

Section: Introductionmentioning

confidence: 94%

Section: Statement Of the Generalized Regularized Problemmentioning

confidence: 99%