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 - <p style="text-align: justify;">This paper is devoted to the study of a nonlinear evolution eddy current model of the type $\partial_t \boldsymbol{B}(\boldsymbol{H})+∇ × (∇ ×&nbsp;\boldsymbol{H}) = 0$ subject to homogeneous Dirichlet boundary conditions $\boldsymbol{H} ×&nbsp;ν=0$ 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 $\boldsymbol{B}(\boldsymbol{H})$.</p>