Abstract
We consider mixed finite element discretizations of linear second-order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations. By a well-known postprocessing technique the discrete problem is equivalent to a modified nonconforming discretization which is solved by preconditioned CG iterations using a multilevel preconditioner in the spirit of Bramble, Pasciak, and Xu designed for standard nonconforming approximations. Local refinement of the triangulations is based on an a posteriori error estimator which can be easily derived from superconvergence results. The performance of the preconditioner and the error estimator is illustrated by several numerical examples.
| Original language | English |
|---|---|
| Pages (from-to) | 1658-1681 |
| Number of pages | 24 |
| Journal | SIAM Journal on Numerical Analysis |
| Volume | 34 |
| Issue number | 4 |
| DOIs | |
| State | Published - 1997 |
| Externally published | Yes |
Keywords
- A posteriori error estimator
- Mixed finite elements
- Multilevel preconditioned cg iterations