**数学与系统科学研究院**

**计算数学所学术报告会**

**报告人：**
Prof. Max Gunzburger

**报告题目：**

Instability of Stabilized Finite Element Methods for the Stokes Problem in the Small Time-step Limit

**报告摘要：**

Recent studies indicate that consistently stabilized methods for unsteady incompressible flows, obtained by a method of lines approach, may experience difficulty when the time step is small relative to the spatial grid size. Using the unsteady Stokes equations as a model problem, we show that the semi-discrete pressure operator associated with such methods is not uniformly coercive. We prove that for sufficiently large (relative to the square of the spatial grid size) time steps, implicit time discretizations contribute terms that stabilize this operator. However, we also prove that if the time step is sufficiently small, then the fully discrete problem necessarily leads to unstable pressure approximations. The semi-discrete pressure operator studied in the paper also arises in pressure-projection methods, thereby making our results potentially useful in other settings. (Joint work with Pavel Bochev and Richard Lehoucq.)

**报告时间：**
2006年6月16日(周五) 上午9:00--10:00

**报告地点：**科技综合楼三层311报告厅

欢迎大家参加!