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We prove that Lin Qun and Lu Tao's splitting extrapolation method and correction method can be effectively applied to raise the accuracy of the numerical solution of elliptic boundary value problems on general regions, i.e., to obtain approximate solutions with fourth- or fifth-order precision in the maximum norm.

The linear nonconforming element and Wilson's element for the obstacle problem are considered. Optimal error bounds for both elements are obtained in the case of regular subdivisions of domain $\Omega$ in $R^2$.

The paper presents some essential results of branch solutions of nonlinear problems and their numerical approximation. The general theory is applied to the bifurcation problems of the Navier-Stokes equations.

The canonical boundary reduction, suggested by Feng Kang, also can be applied to the bidimensional steady Stokes problem. In this paper we first give the representation formula for the solution of the Stokes problem via two complex variable functions. Then by means of complex analysis and the Fourier analysis, we find the expressions of the Poisson integral formulas and the canonical integral equations in three typical domains. From these results the canonical boundary element method for solving the Stokes problem can be developed.

In this paper, we give a recursive algorithm for computing the weighted Moore-Penrose inverse $A^+_{MN}$. This method is a generalization of Greville's method for computing Moore-Penrose inverse $A^+$, and the technique of its proof is new. This method suits the weighted least-squares problem.