A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method
Campos Pinto, Martin ; Dahmen, Wolfgang ; Brix, Kolja
HAL, hal-00320001 / Harvested from HAL
Text on HAL
In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are assumed only to be shape regular but may have hanging nodes subject to certain mild grading conditions. A key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a nonconforming subspace that is controlled by the jumps across the edges.
Publié le : 2008-07-03
Classification:  interior penalty method,  energy-stable splittings,  admissible averaging operators,  frames,  multilevel Schwarz preconditioners,  discontinuous Galerkin methods,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00320001,
     author = {Campos Pinto, Martin and Dahmen, Wolfgang and Brix, Kolja},
     title = {A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method},
     journal = {HAL},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00320001}
}

Campos Pinto, Martin; Dahmen, Wolfgang; Brix, Kolja. A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method. HAL, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/hal-00320001/