论文信息 - Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

Two-Level Schwarz Preconditioners for Super Penalty Discontinuous Galerkin Methods

We extend the construction and analysis of the non-overlapping Schwarz preconditioners proposed in Antonietti et al. [Math. Model. Numer. Anal., 41(1):21-54, 2007] and [Math. Model. Numer. Anal., submitted, 2006] to the (non-consistent) super penalty discontinuos Galerkin methods introduced by Babuska et al. [SIAM J. Numer. Anal., 10:863-875, 1973] and by Brezzi et al. [Numer. Methods Partial Differential Equations, 16(4):365-378, 2000]. We show that the resulting preconditioners are scalable, and we provide the convergence estimates. We also present numerical experiments demonstrating the theoretical results.

Paola F. Antonietti | P. Antonietti | B. Ayuso | Blanca Ayuso

[1] Andrea Toselli,et al. Domain decomposition methods : algorithms and theory , 2005 .

[2] F. Brezzi,et al. Discontinuous Galerkin approximations for elliptic problems , 2000 .

[3] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[4] Susanne C. Brenner,et al. A W-cycle algorithm for a weakly over-penalized interior penalty method , 2007 .

[5] I. Babuska,et al. Nonconforming Elements in the Finite Element Method with Penalty , 1973 .

[6] Paola F. Antonietti,et al. Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations ofElliptic Problems , 2007 .

[7] PAUL CASTILLO,et al. Performance of Discontinuous Galerkin Methods for Elliptic PDEs , 2002, SIAM J. Sci. Comput..

[8] Xiao,et al. MULTIPLICATIVE SCHWARZ ALGORITHMS FOR SOME NONSYMMETRIC AND INDEFINITE PROBLEMS , 1993 .

[9] Susanne C. Brenner,et al. A Weakly Over-Penalized Non-Symmetric Interior Penalty Method , 2007 .

[10] D. Arnold. An Interior Penalty Finite Element Method with Discontinuous Elements , 1982 .

[11] Paola F. Antonietti,et al. Schwarz domain decomposition preconditioners for discontinuous Galerkin approximations of elliptic problems: non-overlapping case , 2007 .

[12] Xiaobing Feng,et al. Two-Level Additive Schwarz Methods for a Discontinuous Galerkin Approximation of Second Order Elliptic Problems , 2001, SIAM J. Numer. Anal..