Elsa Liberman

TL;DR: In this article, the convergence of mixed finite element approximations to the Reissner-Mindlin plate problem is analyzed, and several known elements fall into the analysis, thus providing a unified approach.

TL;DR: This paper considers two lowest-order methods of this family of elements called MITC (mixed interpolation of tensorial components) of Reissner--Mindlin equations based on quadrilateral meshes and obtains optimal H1 and L2 error estimates for both methods.

TL;DR: This paper deals with the approximation of the vibration modes of a plate modelled by the Reissner-Mindlin equations by applying a general approximation theory for spectral problems, and obtains optimal order error estimates for the eigenvectors and the Eigenvalues.

TL;DR: An a posteriori error estimator for a mixed finite element method for the Reissner-Mindlin plate model is presented and it is shown that the estimator yields local lower and global upper bounds of the error in the numerical solution in a natural norm for the problem.

TL;DR: This work considers the approximation of the vibration modes of an elastic plate in contact with a compressible fluid and proves that spurious eigenvalues do not arise with this discretization of Reissner-Mindlin equations.