Functional a Posteriori Error Estimates of Elasticity Problems with Nonlinear Boundary Conditions
Functional a Posteriori Error Estimates of Elasticity Problems with Nonlinear Boundary Conditions
We analyze variational inequalities related to problems in the theory of
elasticity that involve unilateral boundary conditions with or without
friction. We are focused on deriving upper a posteriori estimates of
difference between exact solutions of such type variational inequalities
and any functions lying in the admissible functional class of the
considered problem. These estimates are obtained by a modification of
duality technique earlier used for variational problems with uniformly
convex functionals by S. Repin. We also present a simple two dimensional
axially symmetric problem with a friction boundary condition and derive
analytical solution. Several numerical tests are performed to
demonstrate the quality of our developed estimates.
This is joint cooperation with P. Neittanmaki (Jyvaskyla) and S. Repin
(St. Petersburg).
Literature:
1. Pekka Neittaanmaki, Sergey Repin, Jan Valdman:
Functional a posteriori error estimates of elasticity problems with
nonlinear boundary conditions.
Technical report 13-2011 of the Max Planck Institute for Mathematics in
the Sciences (MIS), Leipzig.
2. Sergey Repin, Jan Valdman:
Functional a posteriori error estimates for problems with nonlinear
boundary conditions.
Journal of Numerical Mathematics 16 (2008), No. 1, 51-81.