Weighted poincaré inequalities and applications in domain decomposition

Lecture Notes in Computational Science and Engineering

Volumn 78 LNCSE, Issue , 2010, Pages 197-204

  Pechstein, Clemens ^a   Scheichl, Robert ^b  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COARSE GRID; DOMAIN DECOMPOSITIONS; MULTIGRID METHODS; PIECEWISE CONSTANT; POINCARE; SECOND-ORDER ELLIPTIC PROBLEM; STANDARD CONDITIONS; SUBDOMAIN;

NUMBER THEORY;

DOMAIN DECOMPOSITION METHODS;

EID: 78651593515     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-642-11304-8_21     Document Type: Conference Paper

References (16)

1. C. R. Dohrmann, A. Klawonn, and O. B. Widlund. Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J. Numer. Anal., 46:2153-2168, 2008.
2. M. Dryja, M. V. Sarkis, and O. B. Widlund. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math., 72:313-348, 1996.
3. Y. Efendiev and J. Galvis. Domain decomposition preconditioners for multiscale problems. Preprint, Texas A&M University, 2009. Submitted.
4. J. Galvis and Y. Efendiev. Domain decomposition preconditioners for multiscale flows in high contrast media. Preprint, Texas A&M University, 2009. Submitted.
5. I. G. Graham, P. Lechner, and R. Scheichl. Domain decomposition for multiscale PDEs. Numer. Math., 106:589-626, 2007.
6. A. Klawonn, O. Rheinbach, and O. B. Widlund. An analysis of a FETI-DP algorithm on irregular subdomains in the plane. SIAM J. Numer. Anal., 46:2484-2504, 2008.
7. A. Klawonn and O. B. Widlund. FETI and Neumann-Neumann iterative substructuring methods: connections and new results. Commun. Pure Appl. Math., 54:57-90, 2001.
8. C. Pechstein and R. Scheichl. Analysis of FETI methods for multiscale PDEs. Numer. Math., 111:293-333, 2008.
9. C. Pechstein and R. Scheichl. Analysis of FETI methods for multiscale PDEs - Part II: Interface variation. BICS Preprint 7/09, University of Bath, 2009. Submitted.
10. C. Pechstein and R. Scheichl. Scaling up through domain decomposition. Appl. Anal., 88(10), 2009.
11. M. Sarkis. Nonstandard coarse spaces and Schwarz methods for elliptic problems with discontinuous coefficients using non-conforming elements. Numer. Math., 77:383-406, 1997.
12. R. Scheichl and E. Vainikko. Additive Schwarz and aggregation-based coarsening for elliptic problems with highly variable coefficients. Computing, 80:319-343, 2007.
13. R. Scheichl, P. S. Vassilevski, and L. Zikatanov. Two-level Schwarz with non-matching coarse grids. Preprint, Lawrence Livermore National Labs, 2009.
14. A. Toselli and O. Widlund. Domain Decomposition Methods - Algorithms and Theory. Springer, Berlin, 2005.
15. J. Van lent, R. Scheichl, and I. G. Graham. Energy minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. Numer. Linear Algebra Appl., 16:775-799, 2009.
16. Y. Zhu. Domain decomposition preconditioners for elliptic equations with jump coefficients. Numer. Linear Algebra Appl., 15:271-289, 2008.