Summary.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received December 13, 2001 / Revised version received February 19, 2002 / Published online June 17, 2002
This work was partially supported by the Norwegian Research Council under projects 128224/431 and SEP-115837/431.
Rights and permissions
About this article
Cite this article
Tai, XC. Rate of Convergence for some constraint decomposition methods for nonlinear variational inequalities. Numer. Math. 93, 755–786 (2003). https://doi.org/10.1007/s002110200404
Issue Date:
DOI: https://doi.org/10.1007/s002110200404