平面理性元的收敛性证明

THE CONVERGENCE PROOF OF THE PLANE RATIONAL FINITE ELEMENT

理性元直接在物理面内列式，并用微分方程的解插值，不用等参技术而在计算面内用多项式插值．由于其解析的特性，即使是不协调元也可证明其收敛性．本文的证明采用力学方法，故易于为力学工作者所接受，且可用于多种单元的结构．收敛性证明可给理性有限元以坚实的理论基础．

The rational finite element formulates directly in the physical domain and interpolates with the solutions, rather than using the iso parametric technique and interpolates with polynomials in the computational plane. Because of its analytical feature, the convergence can still be proved even if the element is incompatible. The present proof makes use of the method in applied mechanics, and is easier to be understood. The method can be extended to structures with multi types of elements. The convergence proof gives a firm theoretical foundation to the rational finite elements.