Least-squares finite element approximations to the Timoshenko beam problem

Jang Jou, Suh Yuh Yang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 H1-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 H1-norm is also briefly discussed.

Original languageEnglish
Pages (from-to)63-75
Number of pages13
JournalApplied Mathematics and Computation
Issue number1
StatePublished - 6 Oct 2000


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