Our research introduces a novel advanced method for fluid computation in complicated domain. It makes use of an advanced polygonal finite element applying equal-order scheme; within each element. Both velocity and pressure fields are represented by a polygonal basis shape function system. This technique is based on a combination of the equal-order mixed scheme method, the polygon finite element method (PFEM) and the adapted local projection method that is used to stabilize the pressure. In order to simulate the fluid flow, MATLAB is utilized for coding and programming. A numerical example of an incompressible fluid flow governed by Stokes system in curved domain is performed to demonstrate the applicability of our developed polygon element. Besides, through the numerical analysis, we show the high flexibility of PFEM for curved domains.

中文翻译：

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曲线域中流体计算的等阶多边形分析

我们的研究为复杂领域的流体计算引入了一种新的先进方法。它利用先进的多边形有限元应用等阶格式；每个元素内。速度场和压力场都由多边形基形函数系统表示。该技术基于等阶混合方案法、多边形有限元法 (PFEM) 和用于稳定压力的自适应局部投影法的组合。为了模拟流体流动，使用MATLAB进行编码和编程。一个由 Stokes 系统在弯曲域中控制的不可压缩流体流动的数值例子被执行，以证明我们开发的多边形单元的适用性。此外，通过数值分析，我们展示了 PFEM 对弯曲域的高度灵活性。