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Multiplicative Schwarz methods for discontinuous Galerkin approximations of elliptic problems. (English) Zbl 1146.65081

The authors study some new multiplicative non-overlapping Schwarz preconditioners for systems of linear algebraic equations arising from a wide class of discontinuous Galerkin (DG) approximations of elliptic boundary-value problems. For symmetric DG approximations, the authors provide optimal convergence bounds for the corresponding error propagation operator. Further, they show that the resulting method can be accelerated by using suitable Krylov space solvers. The issue of preconditioning non-symmetric DG approximations of elliptic problems are discussed. Numerical experiments are carried out in supporting the theoretical results and the efficiency of the proposed preconditioners.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
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References:

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