Adaptive Finite Elements for Elastic Bodies in Contact
SIAM Journal on Scientific Computing
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
SIAM Journal on Numerical Analysis
The Primal-Dual Active Set Strategy as a Semismooth Newton Method
SIAM Journal on Optimization
Scalability and FETI based algorithm for large discretized variational inequalities
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Mixed finite element methods for unilateral problems: convergence analysis and numerical studies
Mathematics of Computation
Quadratic finite element methods for unilateral contact problems
Applied Numerical Mathematics
Hybrid finite element methods for the Signorini problem
Mathematics of Computation
Monotone Multigrid Methods on Nonmatching Grids for Nonlinear Multibody Contact Problems
SIAM Journal on Scientific Computing
Hi-index | 0.00 |
Nonconforming domain decomposition methods and their application to the numerical simulation of non-linear multibody contact problems play an important role in many applications in mechanics. To handle the non-linearity of the contact conditions, we apply a primal-dual active set strategy based on dual Lagrange multipliers. Combining this method with an optimal multigrid for the resulting linear algebraic problems and using inexact strategies, our algorithm yields an efficient iterative solver. Furthermore, we establish, under some regularity assumptions on the solution, optimal convergence orders for the discretization errors for the displacement and the Lagrange multiplier for linear and quadratic finite element spaces; we combine quadratic finite elements with linear and quadratic dual Lagrange multipliers. Several numerical examples confirm our theoretical results. In the last section, we extend our algorithm to a dynamic non-linear multibody contact problem.