Journal of Scientific Computing

, Volume 70, Issue 2, pp 608–630 | Cite as

A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems

  • Paola F. Antonietti
  • Marco Sarti
  • Marco Verani
  • Ludmil T. Zikatanov
Article

Abstract

In this paper we design and analyze a uniform preconditioner for a class of high-order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high-order conforming subspace and results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by numerical tests.

Keywords

Discontinuous Galerkin method High-order discretizations Uniform preconditioning 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Paola F. Antonietti
    • 1
  • Marco Sarti
    • 1
  • Marco Verani
    • 1
  • Ludmil T. Zikatanov
    • 2
    • 3
  1. 1.MOX-Laboratory for Modeling and Scientific Computing, Dipartimento di MatematicaPolitecnico di MilanoMilanItaly
  2. 2.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA
  3. 3.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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