Collocation methods are considered for solving the time-dependent neutron transport equation in two-dimensional planar geometry. Error estimates and stability are derive. Finally, some numerical results are presented.

We considered in [1] the finite element approximation to axial symmetric Stokes flow in a bounded domain. The problem for the flow passing an obstacle in an unbounded domain is also frequently encountered. In this paper, we are going to give approximate solutions for this problem by an approach stated in [2]. An iterative method is used to calculate the combined stiffness matrix.

Continuing the work in [1,2], we discuss the convergence conditions and the error estimates of quasi-conforming elements for linear elasticity problems. Some results about curved elements for second-order boundary value problems are also given.

In this paper, the penalty-nonconforming finite element method for Stokes equations is considered. An abstract error estimate is given. For Crouzeix-Raviart nonconforming triangular elements, in particular, the analysis shows that the "reduced integration" technique is not necessary in the integration of the penalty term on each element. It means that a loss of precision is avoided in this penalty method.

One-dimensional polynomial interpolation does not guarantee the convergency and the stability during numerical computation. For two (or multi)-dimensional interpolation, difficulties are much more raising. There are many fundamental problems, which are left open.
In this paper,we begin with the discussion of reproducing kernel in two variables. With its help we deduce a two-dimensional interpolation formula. According to this formula, the process of interpolation will converge uniformly, whenever the knot system is thickened in finitely. We have also proven that the error function will decrease monotonically in the norm when the number of knot points is increased.
In our formula, knot points may be chosen arbitrarily without any request of regularity about their arrangement. We also do not impose any restriction on the number of knot points. For the case of multi-dimensional interpolation, these features may be important and essential.  

The exact pointwise estimation of the Hermite-Fejér interpolation process based on the zeros of the Jacobi polynomial $P^{(\alpha,\beta)}_n(x)(-1 ‹\alpha,\beta \leq 0)$ is given. The method employed is useful for other extended H-F interpolations also.