论文标题
Oseen和Navier-Stokes方程的超授权伪级有限元方法
Superconvergent pseudostress-velocity finite element methods for the Oseen and Navier-Stokes equations
论文作者
论文摘要
我们提出了与OSEEN方程的伪速度公式的混合有限元方法的先验和超授权误差估计。特别是，我们得出了在非结构化网格下的速度和先验误差估计的超授权估计值，并在某些结构化网格下获得伪造的超偏见结果。多种数值实验验证了理论结果，并说明了基于超对会恢复的自适应网格细化的有效性。还可以从数值上表明，所提出的后处理在不可压缩的Navier-Stokes方程中在基准问题中产生了明显的超级融合。
We present a priori and superconvergence error estimates of mixed finite element methods for the pseudostress-velocity formulation of the Oseen equation. In particular, we derive superconvergence estimates for the velocity and a priori error estimates under unstructured grids, and obtain superconvergence results for the pseudostress under certain structured grids. A variety of numerical experiments validate the theoretical results and illustrate the effectiveness of the superconvergent recovery-based adaptive mesh refinement. It is also numerically shown that the proposed postprocessing yields apparent superconvergence in a benchmark problem for the incompressible Navier--Stokes equation.
