Least-squares finite element approximations to the Timoshenko beam problem

Abstract

In this paper a least-squares finite element method for the Timoshenko beam problem is proposed and analyzed. The method is shown to be convergent and stable without requiring extra smoothness of the exact solutions. For sufficiently regular exact solutions, the method achieves optimal order of convergence in the H-1-norm for all the unknowns (displacement, rotation, shear, moment), uniformly in the small parameter which is generally proportional to the ratio of thickness to length. Thus the locking phenomenon disappears as the parameter tends to zero, A sharp a posteriori error estimator which is exact in the energy norm and equivalent in the H-1-norm is also briefly discussed. (C) 2000 Published by Elsevier Science Inc. All rights reserved. AMS classification: 65N15; 65N30.