Volume 21, Issue 2

We consider a conforming finite element approximation of the Reissner- Mindlin eigenvalue system, for which a robust a posteriori error estimator for the eigenvector and the eigenvalue errors is proposed. For that purpose, we first perform a robust a priori error analysis without strong regularity assumption. Upper and lower bounds are then obtained up to higher order terms that are superconvergent, provided that the eigenvalue is simple. The convergence rate of the proposed estimator is confirmed by a numerical test.

This paper presents a rigorous analysis of the method of computing guaranteed lower bounds of the smallest eigenvalue of an elliptic operator in the case of mixed or purely Neumann boundary conditions. The method was originally invented in [8]. It is based on a decomposition of a domain into a set of overlapping subdomains, for which the corresponding estimates of minimal positive eigenvalues are known or easily computable.We prove that finding a guaranteed lower bound can be reduced to a finite dimensional variational problem. The dimension of the problem depends on the amount of subdomains, and the structure of the corresponding functional depends on topological properties of the set of overlapping subdomains. Several examples show the performance of the estimates.

In this paper, we consider a family of hybrid linear multistep methods (LMM) with reasonable error order for the numerical solution of stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The methods are A(ɑ) -stable for k = 1, ...,9.