Displaying similar documents to “Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case”

Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems

Paola F. Antonietti, Blanca Ayuso (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, and we show that the resulting methods can be accelerated by using suitable Krylov space solvers....

On discontinuous Galerkin method and semiregular family of triangulations

Aleš Prachař (2006)

Applications of Mathematics

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Discretization of second order elliptic partial differential equations by discontinuous Galerkin method often results in numerical schemes with penalties. In this paper we analyze these penalized schemes in the context of quite general triangular meshes satisfying only a semiregularity assumption. A new (modified) penalty term is presented and theoretical properties are proven together with illustrative numerical results.