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

Marián Slodička & Ján Buša Jr

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 $\partial_t \boldsymbol{B}(\boldsymbol{H})+∇ × (∇ × \boldsymbol{H}) = 0$ subject to homogeneous Dirichlet boundary conditions $\boldsymbol{H} × ν=0$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\boldsymbol{B}(\boldsymbol{H})$. 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 $\boldsymbol{B}(\boldsymbol{H})$.

  • Keywords

Electromagnetic field, Nonlinear eddy current problem, Time discretization, Error estimate.

  • AMS Subject Headings

65M15, 83C50.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-26-677, author = {Slodička , Marián and Jr , Ján Buša}, 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 $\partial_t \boldsymbol{B}(\boldsymbol{H})+∇ × (∇ × \boldsymbol{H}) = 0$ subject to homogeneous Dirichlet boundary conditions $\boldsymbol{H} × ν=0$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\boldsymbol{B}(\boldsymbol{H})$. 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 $\boldsymbol{B}(\boldsymbol{H})$.

}, 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 AU - Slodička , Marián AU - Jr , Ján Buša 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, Nonlinear eddy current problem, Time discretization, Error estimate. AB -

This paper is devoted to the study of a nonlinear evolution eddy current model of the type $\partial_t \boldsymbol{B}(\boldsymbol{H})+∇ × (∇ × \boldsymbol{H}) = 0$ subject to homogeneous Dirichlet boundary conditions $\boldsymbol{H} × ν=0$ and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by $\boldsymbol{B}(\boldsymbol{H})$. 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 $\boldsymbol{B}(\boldsymbol{H})$.

Marián Slodička & Ján Buša Jr. (1970). Error Estimates for the Time Discretization for Nonlinear Maxwell's Equations. Journal of Computational Mathematics. 26 (5). 677-688. doi:
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