摘要
本文针对有旋恒定磁场的泊松方程边值问题,给出了基于互补途径的后验误差估计。本文是文献[1]的续篇。求解有旋磁场的困难在于补泛函的前提和强加二类边界条件如何得以满足。本文采用T—Ω算法,提出了一种确定向量位T的具体方法,使向量形式的补泛函极值问题得以转化为标量形式的通常泛函极值问题,从而完成了互补途径的后验误差估计。计算实例针对二类齐次边值问题,以解析解作为精确解,研究了不同节点数时整体误差和局部误差的变化。结果表明,不论是无旋场还是有旋场,基于互补途径的误差估计是可行的。
This paper presents a posteriori error estimate for the boundary-value problems of Piosson equation in magnetostatics based on complementary variational approach. The main difficulties encountered are the prerequisite of the complementary functional and the processing of essential boundary condition of derivative type. The T-Ω method is introduced and a general method of determining the electric vector potential T with zero divergence is presented, so the extremum problem of vector-form complementary functional is reduced to ordinary scalar-form functional. With the analytic solution as exact solution, a model problem with homogeneous boundary condition of derivative type is calculated. It is shown that both local and global errors decrease as the number of nodes are increased, so the error estimates based on the complementary variational approach is feasible.
基金
国家自然科学基金
关键词
后验误差估计
互补变分原理
磁场
有限元分析
A posteriorierror estimate
complementary variational principles
magnetic fields
finite element analysis
