### Abstract

We deal with the solution of the systems of linear algebraic equations arising from Symmetric Interior Penalty discontinuous Galerkin (SIPG) discretization of linear elasticity problems in primal (displacement) formulation. The main focus of the paper is on constructing a uniform preconditioner which is based on a natural splitting of the space of piecewise linear discontinuous functions. The presented approach has recently been introduced in [2] in the context of designing subspace correction methods for scalar elliptic partial differential equations and is extended here to linear elasticity equations, i.e., a class of vector field problems. Similar to the scalar case the solution of the linear algebraic system corresponding to the SIPG method is reduced to the solution of a problem arising from discretization by nonconforming Crouzeix-Raviart elements plus the solution of a well-conditioned problem on the complementary space.

Original language | English (US) |
---|---|

Title of host publication | Numerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers |

Pages | 353-361 |

Number of pages | 9 |

DOIs | |

Publication status | Published - Mar 1 2011 |

Event | 7th International Conference on Numerical Methods and Applications, NMA 2010 - Borovets, Bulgaria Duration: Aug 20 2010 → Aug 24 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 6046 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 7th International Conference on Numerical Methods and Applications, NMA 2010 |
---|---|

Country | Bulgaria |

City | Borovets |

Period | 8/20/10 → 8/24/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Numerical Methods and Applications - 7th International Conference, NMA 2010, Revised Papers*(pp. 353-361). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6046 LNCS). https://doi.org/10.1007/978-3-642-18466-6_42