Abstract
A systematic approach is developed for the selection of the stabilization parameter for stabilized finite element approximation of the Stokes problem, whereby the parameter is chosen to minimize a computable upper bound for the error in the approximation. The approach is applied in the context of both a single fixed mesh and an adaptive mesh refinement procedure. The optimization is carried out by a derivative-free optimization algorithm and is based on minimizing a new fully computable error estimator. Numerical results are presented illustrating the theory and the performance of the estimator, together with the optimization algorithm
| Original language | English |
|---|---|
| Pages (from-to) | 1585-1609 |
| Number of pages | 25 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 51 |
| Issue number | 3 |
| Early online date | 28 May 2013 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords
- stabililzed finite element method
- stabilization parameter
- computable error bounds
- derivative-free optimization