二阶非自伴两点边值问题Garlerkin有限元的超收敛算法

提出了基于改进位移模式的二阶非自伴两点边值问题Garlerkin有限元的超收敛算法. 用常规有限元解的位移模式与高阶有限元解的位移模式之和构造新的位移模式,基于Garlerkin 方法,采用积分形式推导了单元平衡方程. 对于线性单元,本文给出了有代表性的算例,结点和单元的位移、导数都达到了h⁴阶的超收敛精度.

ALGORITHM OF SUPER-CONVERGENCE FOR GALERKIN FEM FOR SECOND ORDER NON-SELF-ADJOINT BOUNDARY-VALUE PROBLEM

An algorithm of super-convergence for the Garlerkin FEM (finite element method) for the second order non-self-adjoint boundary-value problem is proposed based on the improved displacement mode. The new displacement mode is constructed by combining the displacement mode of the conventional finite element and the high-order displacement mode based on the Galerkin method, and the element equilibrium equation is derived using the integral form. A representative example is presented for the Hermite element in this paper, the accuracies of the displacements and the derivatives accuracy of nodes and elements have reached the order of h⁴.