Analysis of a least squares finite element method for the circular arch problem

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Abstract

The stability and convergence of a least squares finite element method for the circular arch problem with shear deformation in a first-order system formulation are investigated. It is shown that the least squares finite element approximations are stable and convergent in a natural energy norm associated with the least squares functional. For the shallow arch case, the optimal order of convergence in the H1-norm for all the unknowns can be achieved uniformly with respect to the small thickness parameter, and thus the locking phenomenon does not occur in this case. A simple and sharp a posteriori error estimator is also addressed.

Original languageEnglish
Pages (from-to)263-278
Number of pages16
JournalApplied Mathematics and Computation
Volume114
Issue number2-3
DOIs
StatePublished - 11 Sep 2000

Keywords

  • A posteriori error estimator
  • Circular arch problem
  • Finite element method
  • Least squares
  • Locking phenomenon

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