不可压Navier-Stokes方程基于误差估算的网格自适应解法

首先导出了广义Stokes方程Petrov—Galerkin有限元数值解的当地事后误差估算公式；以非连续二阶鼓包（bump）函数空间为速度、压强误差的近似空间，该估算基于求解当地单元上的广义Stokes问题。然后，证明了误差估算值与精确误差之间的等价性。最后，将误差估算方法应用于Navier—Stokes环境，以进行不可压粘流计算中的网格自适应处理。数值实验中成功地捕获了多强度物理现象，验证了本文所发展的方法。

A mesh adaptation technique via a posterior error estimate for incompressible Navier-Stokes equations

At first,an a posterior error estimate is derived for Petrov-Galerkin discretization of generalized Stokes equations.This estimate is based on solving a local generalized Stokes problem,using the space of discontinue quadratic bump functions to approximate both velocity and pressure errors.Then,the equivalence between error estimate and exact error is proved.Finally,the estimate is applied in Navier-Stokes environment in order to adapt meshes for the numerical simulation of incompressible viscous fluid flow.Multi-scale phenomena have been captured in numerical experiments that validate the mesh adaptation technique developed for incompressible Navier-Stokes equations.