Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations ofElliptic Problems

Paola F. Antonietti, Blanca Ayuso


In this talk we shall present some multiplicative non-overlapping Schwarz me-thods
for the solution of the linear systems arising from all the discontinuous Galerkin~(DG)
approximations of elliptic problems that have been proposed up to now. In particular,
two-level methods for both symmetric and non-symmetric DG schemes will be introduced and
some interesting features, which have no analog in the conforming case, will be discussed.
Optimal convergence results for the multiplicative Schwarz preconditioners will be presented.
Extensive numerical experiments to validate our theory and to illustrate the performance and
robustness of the proposed two-level methods will be shown.

[DOI: 10.1685/CSC06010] About DOI

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