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

2016 ◽  
Vol 70 (2) ◽  
pp. 608-630 ◽  
Author(s):  
Paola F. Antonietti ◽  
Marco Sarti ◽  
Marco Verani ◽  
Ludmil T. Zikatanov
Keyword(s):  
Discontinuous Galerkin ◽  
Elliptic Problems ◽  
High Order ◽  
Additive Schwarz ◽  
Galerkin Approximations ◽  
Schwarz Preconditioner

scholarly journals On Discontinuous Galerkin Methods for Elliptic Problems with Discontinuous Coefficients

2003 ◽  
Vol 3 (1) ◽  
pp. 76-85 ◽  
Author(s):  
Maksymilian Dryja
Keyword(s):  
Rate Of Convergence ◽  
Discontinuous Galerkin ◽  
Error Bound ◽  
Discontinuous Galerkin Methods ◽  
Elliptic Problems ◽  
Discontinuous Coefficients ◽  
Galerkin Methods ◽  
Additive Schwarz ◽  
Discrete Problems ◽  
Schwarz Preconditioner

AbstractDiscontinuous Galerkin methods for elliptic problems with discontinuous coefficients are discussed. First the error bound of the methods is analyzed. Then a multilevel additive Schwarz preconditioner for one of the discrete problems is designed and analyzed. Although the preconditioner is not optimal it is very well suited for parallel computations and its rate of convergence is independent of the jumps of coefficients.

High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation

2012 ◽  
Vol 11 (2) ◽  
pp. 691-708 ◽  
Author(s):  
Cyril Agut ◽  
Julien Diaz ◽  
Abdelaâziz Ezziani
Keyword(s):  
Wave Equation ◽  
Discontinuous Galerkin ◽  
Time Discretization ◽  
High Order ◽  
High Order Method ◽  
High Order Schemes ◽  
Galerkin Approximations ◽  
Space Discretization ◽  
New Interpretation ◽  
Modified Equation

AbstractWe present a new high order method in space and time for solving the wave equation, based on a new interpretation of the “Modified Equation” technique. Indeed, contrary to most of the works, we consider the time discretization before the space discretization. After the time discretization, an additional biharmonic operator appears, which can not be discretized by classical finite elements. We propose a new Discontinuous Galerkin method for the discretization of this operator, and we provide numerical experiments proving that the new method is more accurate than the classical Modified Equation technique with a lower computational burden.

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