Uniformly convergent iterative methods for discontinuous Galerkin discretizations. (English) Zbl 1203.65242
Summary: We present iterative and preconditioning techniques for the solution of the linear systems resulting from several discontinuous Galerkin (DG) Interior Penalty (IP) discretizations of elliptic problems. We analyze the convergence properties of these algorithms for both symmetric and non-symmetric IP schemes. The iterative methods are based on a “natural” decomposition of the first order DG finite element space as a direct sum of the Crouzeix-Raviart non-conforming finite element space and a subspace that contains functions discontinuous at interior faces. We also present numerical examples confirming the theoretical results.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65F08 | Preconditioners for iterative methods |
| 65F10 | Iterative numerical methods for linear systems |
| 65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
Keywords:
discontinuous Galerkin finite element methods; subspace correction methods; interior penalty methods; iterative methods for non-symmetric problemsReferences:
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