A hierarchical domain decomposition preconditioner for \(h\)-\(p\) finite element approximation on locally refined meshes. (English) Zbl 0860.65111
The author gives a preconditioner for domain decomposition of an \(h\)-\(p\) refinement of a finite element approximation that is a generalisation of preconditioners for \(h\)- and \(p\)-refinements. He gives a bound for the condition number of the preconditioned system that includes earlier results. Numerical examples are included.
Reviewer: J.D.P.Donnelly (Oxford)
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |
