Penalty finite element method for Stokes problem with nonlinear slip boundary conditions
Penalty finite element method for Stokes problem with nonlinear slip boundary conditions
复制标题
DOI：
10.1016/j.amc.2008.06.035
复制
发表时间：
2008-10
期刊：
影响因子：
--
通讯作者：
Yuan Li;Kaitai Li
中科院分区：
文献类型：
--
作者：
Yuan Li;Kaitai Li
基于满足离散inf-sup条件的有限元子空间（Vh，Mh），研究了具有非线性滑移边界条件的Stokes问题的罚有限元方法。由于这类非线性滑移边界条件具有次微分性质，因此与Stokes问题相关的弱变分形式是变分不等式。在一定的正则性假设下，得到了u和uh之间以及u和uh之间的最优H1和L2误差估计，其中H1误差的误差阶为ε+h，L2误差的误差阶为ε+ h2.
The penalty finite element method for Stokes problem with nonlinear slip boundary conditions, based on the finite element subspace (Vh,Mh) which satisfies the discrete inf–sup condition, is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation associated with Stokes problem is variational inequality. Under some regularity assumptions, we obtain the optimal H1and L2error estimates between u and uh, and between u and uhε, where the error orders are ε+h for H1error and ε+h2for L2error.