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中文摘要：
有限元离散一类速度追踪问题后得到具有鞍点结构的线性系统，针对该鞍点系统，本文提出了一种新的分裂迭代技术．证明了新的分裂迭代方法的无条件收敛性，详细分析了新的分裂预条件子对应的预处理矩阵的谱性质．数值结果验证了对于大范围的网格参数和正则参数，新的分裂预条件子在求解有限元离散速度追踪问题得到的鞍点系统时的可行性和有效性．
英文摘要：
We develop a new splitting iterative method and a splitting preconditioner for the saddle point system arising from the finite element discretization for the velocity tracking problem. It is proved that the new splitting iterafive method converges unconditionally. The spectral properties of the matrix preconditioned by the splitting preconditioner are analyzed. Furthermore, the theoretical results are confirmed by numerical experiments, which demonstrate that the new preconditioner is feasible and effective for the the linear system arising from the finite element discretization equations of the velocity tracking problem for a wide range of mesh sizes and regulafization parameters.
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