Volume 26, Issue 5
Error Estimates for the Time Discretization for Nonlinear Maxwell's Equations
DOI:

J. Comp. Math., 26 (2008), pp. 677-688

Published online: 2008-10

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• Abstract

This paper is devoted to the study of a nonlinear evolution eddy current model of the type $\D\partial_t\vector{B}(\vector{H})+\rotor\left(\rotor\vector{H}\right) =\vector{0}$ subject to homogeneous Dirichlet boundary conditions $\vector{H}\times\normal=\vector{0}$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\vector{B}(\vector{H})$. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of $\vector{B}(\vector{H})$.

• Keywords

Electromagnetic field Nonlinear eddy current problem Time discretization Error estimate

65M15 83C50.

@Article{JCM-26-677, author = {}, title = {Error Estimates for the Time Discretization for Nonlinear Maxwell's Equations}, journal = {Journal of Computational Mathematics}, year = {2008}, volume = {26}, number = {5}, pages = {677--688}, abstract = { This paper is devoted to the study of a nonlinear evolution eddy current model of the type $\D\partial_t\vector{B}(\vector{H})+\rotor\left(\rotor\vector{H}\right) =\vector{0}$ subject to homogeneous Dirichlet boundary conditions $\vector{H}\times\normal=\vector{0}$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\vector{B}(\vector{H})$. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of $\vector{B}(\vector{H})$.}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8651.html} }
TY - JOUR T1 - Error Estimates for the Time Discretization for Nonlinear Maxwell's Equations JO - Journal of Computational Mathematics VL - 5 SP - 677 EP - 688 PY - 2008 DA - 2008/10 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8651.html KW - Electromagnetic field KW - Nonlinear eddy current problem KW - Time discretization KW - Error estimate AB - This paper is devoted to the study of a nonlinear evolution eddy current model of the type $\D\partial_t\vector{B}(\vector{H})+\rotor\left(\rotor\vector{H}\right) =\vector{0}$ subject to homogeneous Dirichlet boundary conditions $\vector{H}\times\normal=\vector{0}$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\vector{B}(\vector{H})$. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of $\vector{B}(\vector{H})$.