Based on full domain partition technique, some parallel iterative pressure projection stabilized finite element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions are designed and analyzed. In these algorithms, the lowest equal‐order P₁ − P₁ elements are used for finite element discretization and a local pressure projection stabilized method is used to counteract the invalidness of the discrete inf‐sup condition. Each subproblem is solved on a global composite mesh with the vast majority of the degrees of freedom associated with the particular subdomain that it is responsible for and hence can be solved in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. We estimate the optimal error bounds of the approximate solutions with the use of some (strong) uniqueness conditions. Numerical results are also given to demonstrate the effectiveness of the parallel algorithms.

中文翻译：

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带有非线性滑移边界条件的Navier-Stokes方程的并行迭代稳定有限元算法

基于全域分割技术，设计并分析了带有非线性滑移边界条件的Navier-Stokes方程的并行并行迭代压力投影稳定化有限元算法。在这些算法中，最低等阶P ₁  -  P ₁有限元离散化使用有限元法，局部压力投影稳定化方法用于抵消离散注入条件的无效性。每个子问题都在全局复合网格上求解，该网格具有与它负责的特定子域相关的绝大多数自由度，因此可以使用现有的顺序求解器与其他子问题并行求解，而无需进行大量重新编码。所有的子问题都是非线性的，可以通过三种迭代方法独立解决。我们使用一些（强）唯一性条件来估计近似解的最佳误差范围。数值结果也证明了并行算法的有效性。