7 research outputs found
Mortaring for linear elasticity using mixed and stabilized finite elements
The purpose of this work is to study mortar methods for linear elasticity
using standard low order finite element spaces. Based on residual
stabilization, we introduce a stabilized mortar method for linear elasticity
and compare it to the unstabilized mixed mortar method. For simplicity, both
methods use a Lagrange multiplier defined on a trace mesh inherited from one
side of the interface only. We derive a quasi-optimality estimate for the
stabilized method and present the stability criteria of the mixed
approximation. Our numerical results demonstrate the stability and the
convergence of the methods for tie contact problems. Moreover, the results show
that the mixed method can be successfully extended to three dimensional
problems
On Nitsche's method for elastic contact problems
We show quasi-optimality and a posteriori error estimates for the
frictionless contact problem between two elastic bodies with a zero-gap
function. The analysis is based on interpreting Nitsche's method as a
stabilised finite element method for which the error estimates can be obtained
with minimal regularity assumptions and without the saturation assumption. We
present three different Nitsche's mortaring techniques for the contact boundary
each corresponding to a different stabilising term. Our numerical experiments
show the robustness of Nitsche's method and corroborates the efficiency of the
a posteriori error estimators
Mixed and Stabilized Finite Element Methods for the Obstacle Problem
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.Peer reviewe