中文摘要：

基于低顺序的一致有限元素 subspace ( V [ h ]， M [ h ])例如 P [ 1 ]-P[0]三角元素或 Q [ 1 ]-P[0]四边的元素，为Stokes 问题与的局部地稳定的有限元素方法非线性滑动边界条件在这份报纸被调查。为这个班非线性包括 subdifferential 性质滑动边界条件，与 Stokes 问题联系的弱变化明确的表达是变化不平等。自从(V [h ] ， M [h ]) 不满足分离 inf 啜条件，一个宏元素条件为构造局部地稳定的明确的表达被介绍以便稳定性(V [h ] ， M [h ]) 被建立。在这些条件下面，我们获得 H [1 ] 并且 L [2 ] 为数字答案的错误估计。[从作者抽象]

英文摘要：

Based on the low-order conforming finite element subspace （Vh, Mh） such as the P1-P0 triangle element or the Q1-P0 quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since （Vh, Mh） does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of （Vh, Mh） is established. Under these conditions, we obtain the H1 and L2 error estimates for the numerical solutions.