Title: Rate of Convergence for some constraint decomposition methods for nonlinear variational inequalities

Author: Xue--Cheng Tai


Abstract:
Some general subspace correction algorithms are proposed for a convex
optimization problem
over a convex constraint subset. One of the nontrivial applications of
the algorithms is the
solving of some obstacle problems by multilevel domain decomposition and
multigrid methods.
For domain decomposition and multigrid methods, the rate of
convergence for the algorithms for obstacle problems is of the same
order as the rate of convergence for jump coefficient linear elliptic
problems. In order to analyse the convergence rate, we need to decompose
a finite element function into a sum of functions from the subspaces and
also satisfying some constraints. A special nonlinear interpolation operator
is introduced for decomposing the functions.