Two-level non-overlapping Schwarz preconditioners for a discontinuous Galerkin approximation of the biharmonic equation. (English) Zbl 1072.65161
The authors propose and analyse two-level non-overlapping aditive and multiplicative Schwarz methods for the discontinuous Galerkin approximation of a class of fourth order elliptic partial differential equations. Based on a trace inequality and a generalized Poincaré inequality for picewise \(H^1\) functions, as well as an approximation property of picewise constant functions, the authors prove that for quasi-uniform discretizations the condition number of the system with the two level Schwarz preconditioners are of order \({\mathcal{O}}((H/h)^3)\).
Reviewer: Constantin Popa (Constanta)
MSC:
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 65F10 | Iterative numerical methods for linear systems |
| 65F35 | Numerical computation of matrix norms, conditioning, scaling |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J40 | Boundary value problems for higher-order elliptic equations |
Keywords:
biharmonic equation; discontinuous Galerkin methods; Schwarz methods; domain decomposition; preconditioning; fourth order elliptic equations; condition numberReferences:
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