Date:

Monday, March 18, 2002

Speaker:

Dr. Xue-Cheng Tai

Affiliation:

University of Bergen, Norway (currently visiting UCLA)

Web Page

http://www.mi.uib.no/~tai

Title:

Mesh independent convergence algorithms for variational inequalities

Abstract:

Domain decomposition and multigrid methods have been intensively used for solving partial diffferential equations. Mesh independent convergence has been observed in computations and there is also a very rich literature for the analysis. Here, we are concerned about using these methods for strongly nonlinear problems. The nonlinearity not only comes from the differential operator, but also comes from the fact that the solution must satisfy a convex constraint. How to use domain decomposition and multigird method to deal with the nonlinear operators and to deal with the constraint imposed on the solution is still a difficult problem for many concrete applications. In this talk, we will show some of the success and failures we have encountered in dealing with these problems. The essential contribution is to give a theoritical justification that some of the algorithms do have the same order of convergece compared with the corresponding algorithms for some corresponding linear prolems.