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 language | English |
|---|---|
| Pages (from-to) | 263-278 |
| Number of pages | 16 |
| Journal | Applied Mathematics and Computation |
| Volume | 114 |
| Issue number | 2-3 |
| DOIs | |
| State | Published - 11 Sep 2000 |
Keywords
- A posteriori error estimator
- Circular arch problem
- Finite element method
- Least squares
- Locking phenomenon