Convergence of a Contact-Neumann Iteration for the Solution of Two-Body Contact Problems
Authors:
- 1 August 2003
- journal article
- research article
- Published by World Scientific Pub Co Pte Ltd in Mathematical Models and Methods in Applied Sciences
- Vol. 13 (08) , 1103-1118
Abstract
We study an iteration for the solution of two-body contact problems without friction based on one-sided contact problems for one body and Neumann problems for the other one. The convergence of this iteration is proved in the continuous setting by reformulating it as a fixed point iteration for a contractive operator. In addition, the application of the method with mortar finite elements is discussed, and the convergence of the corresponding discrete iteration is verified.Keywords
This publication has 25 references indexed in Scilit:
- On a splitting type algorithm for the numerical realization of contact problems with Coulomb frictionComputer Methods in Applied Mechanics and Engineering, 2002
- Algorithme de Neumann–Dirichlet pour des problèmes de contact unilatéral : Résultat de convergenceComptes Rendus Mathematique, 2002
- Adaptive multigrid methods for Signorini's problem in linear elasticityComputing and Visualization in Science, 2001
- Stability and patch test performance of contact discretizations and a new solution algorithmComputers & Structures, 2001
- A superlinear convergent augmented Lagrangian procedure for contact problemsEngineering Computations, 1999
- A method for solving contact problemsInternational Journal for Numerical Methods in Engineering, 1998
- An augmented Lagrangian method for discrete large‐slip contact problemsInternational Journal for Numerical Methods in Engineering, 1993
- An augmented lagrangian treatment of contact problems involving frictionComputers & Structures, 1992
- A mathematical programming approach to three-dimensional contact problems with frictionComputer Methods in Applied Mechanics and Engineering, 1986
- A solution method for static and dynamic analysis of three-dimensional contact problems with frictionComputers & Structures, 1986