Navier-Stokes方程的局部压力梯度稳定化有限元方法分析(英文)

Analysis of a local pressure gradient-stabilized finite element approximation of the Navier-Stokes equations

基于局部压力梯度稳定化方法,作者提出了Navier-Stokes方程的一种新的有限元方法,其中速度V属于H^1连续的空间,压力P属于L^2非连续的空间.利用Brouwer不动点定理,作者证明了离散解的存在性和唯一性并给出了误差估计.

Based on local pressure gradient-stabilized finite element method, the authors develop a new approximation of the Navier-Stokes equations, of which the velocity is in continuous H1 space and pressure in discontinuous L2 space. By using Brouwer＇s fixed point theorem, the authors prove the existence and uniqueness of the discrete solution and give the error estimates.