We give a new justification of the linear membrane and flexural shell models. We prove that the sequence of scaled energy functionals associated with the scaled problem Γ-converges to the energy functional associated with a two-dimensional model. This two-dimensional model is a membrane or flexural one, depending on the geometric and kinematic conditions. Then, a classical argument allows to give a new proof of the convergence theorems recently obtained by P.G. Ciarlet, V. Lods and B. Miara.

In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived.

A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated.  

In this paper parallel Rosenbrock methods in real-time simulation are presented on parallel computers. Their construction, their convergence and their numerical stability are studied, and the numerical simulation experiments are conducted on a personal computer and a parallel computer respectively.

In this paper, an algorithm for computing some of the largest (smallest) generalized eigenvalues with corresponding eigenvectors of a sparse symmetric positive definite matrix pencil is presented. The algorithm uses an iteration function and inverse power iteration process to get the largest one first, then executes $m-1$ Lanczos-like steps to get initial approximations of the next $m-1$ ones, without computing any Ritz pair, for which a procedure combining Rayleigh quotient iteration with shifted inverse power iteration is used to obtain more accurate eigenvalues and eigenvectors. This algorithm keeps the advantages of preserving sparsity of the original matrices as in Lanczos method and RQI and converges with a higher rate than the method described in [12] and provides a simple technique to compute initial approximate pairs which are guaranteed to converge to the wanted $m$ largest eigenpairs using RQI. In addition, it avoids some of the disadvantages of Lanczos and RQI, for solving extreme eigenproblems. When symmetric positive definite linear systems must be solved in the process, an algebraic multilevel iteration method (AMLI) is applied. The algorithm is fully parallelizable.  

In this paper we present a $C^1$ interpolation scheme on a triangle. The interpolant assumes given values and one order derivatives at the vertices of the triangle. It is made up of partial interpolants blended with corresponding weight functions. Any partial interpolant is a piecewise cubics defined on a split of the triangle, while the weight function is just the respective barycentric coordinate. Hence the interpolant can be regarded as a piecewise quartic. We device a simple algorithm for the evaluation of the interpolant. It's easy to represent the interpolant with B-net method. We also depict the Franke's function and its interpolant, the illustration of which shows good visual effect of the scheme.  

In this paper, we discuss a posteriori error estimates of the eigenvalue $\lambda_h$ given by Adini nonconforming finite element. We give an asymptotically exact error estimator of the $\lambda_h$. We prove that the order of convergence of the $\lambda_h$ is just 2 and the $\lambda_h$ converge from below for sufficiently small $h$.  

This paper presents optimum a one-parameter iteration (OOPI) method and a multi-parameter iteration direct (MPID) method for efficiently solving linear algebraic systems with low order matrix $A$ and high order matrix $B: Y = (A \otimes B)Y+\Phi$. On parallel computers (also on serial computer) the former will be efficient, even very efficient under certain conditions, the latter will be universally very efficient.

In this paper, we solve a problem on the existence of conjugate symplecticity of linear multi-step methods (LMSM), the negative result is obtained.

The generalized least squares (LS) problem  $$\min_{x\in R^n} (Ax-b)^T W^{-1} (Ax-b)$$ appears in many application areas. Here $W$ is an $m \times m$ symmetric positive definite matrix and $A$ is an $m \times n$ matrix with $m ≥ n$. Since the problem has many solutions in rank deficient case, some special preconditioned techniques are adapted to obtain the minimum 2-norm solution. A block SOR method and the preconditioned conjugate gradient (PCG) method are proposed here. Convergence and optimal relaxation parameter for the block SOR method are studied. An error bound for the PCG method is given. The comparison of these methods is investigated. Some remarks on the implementation of the methods and the operation cost are given as well.