A Unified Analysis of Balancing Domain Decomposition by Constraints for Discontinuous Galerkin Discretizations


The BDDC algorithm is extended to a large class of discontinuous Galerkin (DG) discretizations of second order elliptic problems. An estimate of $C(1+\log(H/h))^2$ is obtained for the condition number of the preconditioned system where $C$ is a constant independent of $h$ or $H$ or large jumps in the coefficient of the problem. Numerical simulations are presented which confirm the theoretical results. A key component for the development and analysis of the BDDC algorithm is a novel perspective presenting the DG discretization as the sum of elementwise „local” bilinear forms. The elementwise perspective allows for a simple unified analysis of a variety of DG methods and leads naturally to the appropriate choice for the subdomainwise local bilinear forms. Additionally, this new perspective enables a connection to be drawn between the DG discretization and a related continuous finite element discretization to simplify the analysis of the BDDC algorithm.


  1. discontinuous Galerkin
  2. domain decomposition
  3. BDDC

MSC codes

  1. 65M55
  2. 65M60
  3. 65N30
  4. 65N55

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Published In

cover image SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Pages: 1695 - 1712
ISSN (online): 1095-7170


Submitted: 20 October 2010
Accepted: 25 April 2012
Published online: 21 June 2012


  1. discontinuous Galerkin
  2. domain decomposition
  3. BDDC

MSC codes

  1. 65M55
  2. 65M60
  3. 65N30
  4. 65N55



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