Mixed and Stabilized Finite Element Methods for the Obstacle Problem

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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.
Original languageEnglish
Title of host publicationConference proceedings of the Emerging Trends in Applied Mathematics and Mechanics
Publication statusPublished - 2016
MoE publication typeD3 Professional conference proceedings
EventEmerging Trends in Applied Mathematics and Mechanics - Perpignan, France
Duration: 30 May 20163 Jun 2016

Conference

ConferenceEmerging Trends in Applied Mathematics and Mechanics
Abbreviated titleETAMM
CountryFrance
CityPerpignan
Period30/05/201603/06/2016

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