Least Squares for the Perturbed Stokes Equations and the Reissner--Mindlin Plate

Least Squares for the Perturbed Stokes Equations and the Reissner-Mindlin Plate

In this paper, we develop two least-squares approaches for the solution of the Stokes equations perturbed by a Laplacian term. (Such perturbed Stokes equations arise from finite element approximations of the Reissner–Mindlin plate.) Both are two-stage algorithms that solve first for the curls of the rotation of the fibers and the solenoidal part of the shear strain, then for the rotation itself...

Least-squares finite element approximations for the Reissner-Mindlin plate

1Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, IN 47907-1395, USA. Email: [email protected]. 2Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA. Email: [email protected]. 3MAB, CNRS UPRESA 5466, Université de Bordeaux I, 351 Cours de la Libération, 33400 Takence, France. Email: hzhang@m...

Finite Elements for the Reissner-Mindlin Plate

A negative-norm least squares method for Reissner-Mindlin plates

In this paper a least squares method, using the minus one norm developed by Bramble, Lazarov, and Pasciak, is introduced to approximate the solution of the Reissner-Mindlin plate problem with small parameter t, the thickness of the plate. The reformulation of Brezzi and Fortin is employed to prevent locking. Taking advantage of the least squares approach, we use only continuous finite elements ...

Wilson's element for the Reissner-Mindlin plate

A new method for the Reissner-Mindlin plate has been proposed. The nonconform-ing Wilson element is used for transverse displacement, rotation is approximated by the usual bilinear element, and an orthogonal projection is applied to the shear stress term. The uniform convergence with respect to the plate thickness is established. Numerical results are provided. The new method is simple in imple...