摘要
互补变分原理用于有限元近似解的后验误差估计,从原理本身看是整体误差估计,将其用于局部误差估计是否可行,仍需研究。为此,本文对恒定磁场的拉普拉斯方程非齐次混合边值模型题进行了研究,给出了互补泛函的有限元离散格式,提出了对补泛函中强加二类边界条件的处理方法,解决了互补问题中标量位和向量位的匹配问题;通过逐步加密网格和逐个单元的计算,并与解析解对比,验证了互补变分原理对局部误差估计的可行性。
In this paper, on the basis of complementary variational princi-
ples, the inhomogeneous mixed boundary value problem of Laplace
equation in stationary magnetic field is investigated, the FE discre-
tization formulae of complementary functionals are given. Using the
air gap field of a single slotted armature as a modle problem, the
values of complementary functionals are calculated, the magnetic induc-
tions in nodes for two kinds of functional by numerical calculation
are compared with analytic solution. Finally, the global and local
error estimates are given and analysed. It is shown that assessing the
local errors by use of complementary variational principles is possible.
基金
国家自然科学基金
关键词
恒定磁场
互补变分原理
误差估计
posteriori error estimation
complementary variational principle
FE calcution of stationary magnetic field
