## Abstract

For the obstacle problem we consider two classes of finite element methods, a

mixed and a stabilized formulation. In the mixed formulation the contact force is an independent variable and we have a classical saddle point formulation covered by the Babuska-Brezzi theory. We prove the necessary inf-sup condition for a family of finite element spaces. Using this result, an a priori error estimate is derived. In addition, we derive an a posteriori estimate.

The other class is based on a stabilized formulation. The advantage of this is that an arbitrary choice of finite element spaces can be used. We prove this rigorously by stability and a priori estimates. We also prove an a posteriori estimate. For both methods the estimates are confirmed by numerical computations.

mixed and a stabilized formulation. In the mixed formulation the contact force is an independent variable and we have a classical saddle point formulation covered by the Babuska-Brezzi theory. We prove the necessary inf-sup condition for a family of finite element spaces. Using this result, an a priori error estimate is derived. In addition, we derive an a posteriori estimate.

The other class is based on a stabilized formulation. The advantage of this is that an arbitrary choice of finite element spaces can be used. We prove this rigorously by stability and a priori estimates. We also prove an a posteriori estimate. For both methods the estimates are confirmed by numerical computations.

Original language | English |
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Title of host publication | Conference proceedings of the Emerging Trends in Applied Mathematics and Mechanics |

Publication status | Published - 2016 |

MoE publication type | D3 Professional conference proceedings |

Event | Emerging Trends in Applied Mathematics and Mechanics - Perpignan, France Duration: 30 May 2016 → 3 Jun 2016 |

### Conference

Conference | Emerging Trends in Applied Mathematics and Mechanics |
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Abbreviated title | ETAMM |

Country | France |

City | Perpignan |

Period | 30/05/2016 → 03/06/2016 |