Mixed finite element methods for unilateral problems: convergence analysis and numerical studies
Open Access
- 21 May 2001
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 71 (237), 1-26
- https://doi.org/10.1090/s0025-5718-01-01318-7
Abstract
In this paper, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. The discretized unilateral conditions at the candidate contact interface are expressed by using either continuous piecewise linear or piecewise constant Lagrange multipliers in the saddle-point formulation. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.This publication has 10 references indexed in Scilit:
- Numerical implementation of two nonconforming finite element methods for unilateral contactComputer Methods in Applied Mechanics and Engineering, 2000
- An Introduction to Variational Inequalities and Their ApplicationsPublished by Society for Industrial & Applied Mathematics (SIAM) ,2000
- Méthodes d'éléments finis pour des inéquations variationnelles de contact unilatéralComptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1999
- EXTENSION OF THE MORTAR FINITE ELEMENT METHOD TO A VARIATIONAL INEQUALITY MODELING UNILATERAL CONTACTMathematical Models and Methods in Applied Sciences, 1999
- A propos d'approximation par elements finis optimale pour les problèmes de contact unilatéralComptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998
- Domain Decomposition with Nonmatching Grids: Augmented Lagrangian ApproachMathematics of Computation, 1995
- The Finite Element Method for Elliptic ProblemsJournal of Applied Mechanics, 1978
- Error estimates for the finite element solution of variational inequalitiesNumerische Mathematik, 1978
- Error estimates for the finite element solution of variational inequalitiesNumerische Mathematik, 1977
- A Tight Upper Bound on the Rate of Convergence of Frank-Wolfe AlgorithmSIAM Journal on Control, 1968