论文标题
通用网格上的navier-stokes方程的Morley型虚拟元素方法
The Morley-type virtual element method for the Navier-Stokes equations in stream-function form on general meshes
论文作者
论文摘要
设计了不可压缩的Navier-Stokes方程的不合格的Morley型虚拟元素方法，该方程设计了简单连接的多边形域（不一定是凸）上的流函数。通过使用新的丰富操作员进行严格的分析。更确切地说，通过使用此类操作员，我们提供了新颖的离散SOBOLEV嵌入式，可以建立离散方案的良好性，并在损坏的$ H^2 $ - ，$ H^1 $ - 和$ h^1 $ - 和$ l^2 $ -NORMS中获得最佳的误差估计，并在弱解决方案上的最小规则条件下。速度和涡度场是通过后处理公式恢复的。此外，提出了一种基于Stokes复合序列的新算法用于压力恢复。对于所有后处理变量，获得了最佳误差估计。最后，通过多个基准测试验证了理论误差界限和该方法的良好性能。
The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis by using a new enriching operator is developed. More precisely, by employing such operator, we provide novel discrete Sobolev embeddings, which allow to establish the well-posedness of the discrete scheme and obtain optimal error estimates in broken $H^2$-, $H^1$- and $L^2$-norms under minimal regularity condition on the weak solution. The velocity and vorticity fields are recovered via a postprocessing formulas. Furthermore, a new algorithm for pressure recovery based on a Stokes complex sequence is presented. Optimal error estimates are obtained for all the postprocessed variables. Finally, the theoretical error bounds and the good performance of the method are validated through several benchmark tests.
