Analysis of a least squares finite element method for the circular arch problem1

摘要

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.