3维非定常Navier-Stokes方程组高效全离散有限元方法研究进展

Research Progress in the Highly Efficient Fully Discrete Finite Element Method for Solving the 3D Time-Dependent Navier-Stokes Equations

针对数值求解3维非定常Navier-Stokes方程组时面临的不可压缩条件、非线性和长时间积分性等困难,讨论了能够克服这些困难的高效全离散有限元方法的研究现状和最新研究成果.此外,也阐述了求解3维非定常Navier-Stokes方程组的有限元空间离散解的稳定性、误差估计和高效全离散有限元解的最优误差估计.

Main difficulties of numerically solving the 3D time-dependent Navier-Stokes equations are incompressibility condition,nonlinearity and longtime integration.First,we discuss the research progress and recent achievements in the highly efficient fully discrete finite element method for solving the 3D time-dependent NavierStokes equations.Secondly,we expound the stability and error estimates of the finite element spatial discrete solution and the optimal error estimates of the highly efficient fully discrete finite element method for solving the3D time-dependent Navier-Stokes equations.