Poisson方程的Q_1^(rot)元和NF_1元特征值法

EIGENVALUE METHODS OF SOLVING POISSON EQUATIONS WITH Q_1^(rot) ELEMENT AND NF_1 ELEMENT

本文给出用三维非协调元的特征值方法求解一般的二阶椭圆边值问题的数值计算方法,从而验证了非协调元的收敛性的理论正确性及三维Q_1^(rot)元特征值误差渐进展开式的正确性.本文的数值实验表明:三维Q_1^(rot)元外推特征值下逼近准确特征值;三维NF_1元特征值和外推特征值都下逼近准确特征值;三维Q_1^(rot)元和三维NF_1元二网格离散方案特征值既下逼近准确特征值又上逼近准确特征值;三维Q_1^(rot)元比三维NF_1元有较好的数值表现.

In this paper, some numerical computational methods of eigenvalue methods of three- dimensional non-conforming element for the general second-order elliptic boundary value problems are derived, moreover, the three-dimensional Q1^rot non-conforming element asymptotic expansion theory for eigenvalue problem is demonstrated with some numerical experiments. It is shown by the numerical experiments results that the three-dimensional Q1^rot non- conforming element extrapolation eigenvalues approximate exact eigenvalues from below, the three-dimensional NF1 non-conforming element eigenvalues and extrapolation eigenvalues approximate exact eigenvalues from below, the three-dimensional Q1^rot non-conforming ele- ment and the three-dimensional NF1 non-conforming element two-grid discretization schemes eigenvalues approximate exact eigenvalues not only from below but also from above, and the numerical accuracy of three-dimensional Q1^rot non-conforming element is much better than that of the three-dimensional NF1 non-conforming element.