数学与系统科学研究院

计算数学所学术报告

报告人：        Xuecheng Tai

Univ of Bergen, Norway

报告题目 Nonlinear positive interpolation operators and mesh independent algorithms for variational inequalities

Abstract: First, we introduce some nonlinear positive and negative interpolation operators. The interpolation need to preserve positivity or negativity of a function. In addition, the interpolation must be pointwisely below or above the function. Some of the operators also have the pointwise monotone property over refined meshes. It is also desirable that the interpolation have the needed approximation and stability estimates. In the second part, 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. The nonlinear interpolation operator is used for decomposing the functions.

报告时间：2004年6月17日  下午4：00

报告地点：科技综合楼三层报告厅