TY - JOUR
T1 - An a posteriori error estimator for two-body contact problems on non-matching meshes
AU - Wohlmuth, Barbara I.
N1 - Funding Information:
This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, B8.
PY - 2007/10
Y1 - 2007/10
N2 - A posteriori error estimates for two-body contact problems are established. The discretization is based on mortar finite elements with dual Lagrange multipliers. To define locally the error estimator, Arnold-Winther elements for the stress and equilibrated fluxes for the surface traction are used. Using the Lagrange multiplier on the contact zone as Neumann boundary conditions, equilibrated fluxes can be locally computed. In terms of these fluxes, we define on each element a symmetric and globally H(div)-conforming approximation for the stress. Upper and lower bounds for the discretization error in the energy norm are provided. In contrast to many other approaches, the constant in the upper bound is, up to higher order terms, equal to one. Numerical examples illustrate the reliability and efficiency of the estimator.
AB - A posteriori error estimates for two-body contact problems are established. The discretization is based on mortar finite elements with dual Lagrange multipliers. To define locally the error estimator, Arnold-Winther elements for the stress and equilibrated fluxes for the surface traction are used. Using the Lagrange multiplier on the contact zone as Neumann boundary conditions, equilibrated fluxes can be locally computed. In terms of these fluxes, we define on each element a symmetric and globally H(div)-conforming approximation for the stress. Upper and lower bounds for the discretization error in the energy norm are provided. In contrast to many other approaches, the constant in the upper bound is, up to higher order terms, equal to one. Numerical examples illustrate the reliability and efficiency of the estimator.
KW - A posteriori error estimates
KW - Contact problems
KW - Equilibrated fluxes
KW - Mixed finite elements
KW - Mortar methods
KW - Non-matching meshes
UR - http://www.scopus.com/inward/record.url?scp=34548449391&partnerID=8YFLogxK
U2 - 10.1007/s10915-007-9139-7
DO - 10.1007/s10915-007-9139-7
M3 - Article
AN - SCOPUS:34548449391
SN - 0885-7474
VL - 33
SP - 25
EP - 45
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -