非线性麦克斯韦方程时域离散化的一种误差估计算法

An Error Estimate Algorithm for the Time Discretization of Nonlinear Maxwell's Equations

以非线性变化的渦电流的麦克斯韦方程为例,提出了在满足齐次狄利克雷边界条件和给定初始值情况下,采用后向欧拉方法进行时域离散化的方法,对利普希茨连续情形的误差进行了计算,并在适当的函数空间得到了误差估计.数值仿真表明,误差估计结果依赖于B(H)的非线性特性,而且能快速收敛.

Taking a nonlinear evolution eddy current Maxwell＇s equations as the example ,the backward Euler method for the time discretization is proposed subjecting to homogeneous Dirichlet boundary conditions and a given initialvalue. The error estimate for Lipschitz continuous case is computed and achieved in suitable function spaces. The numerical simulation shows that the error estimate results depend on the nonlinearity of B（H） and can convergence speedly.