**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