可压缩Navier-Stokes方程的稳定化有限元方法

Stabilized mixed methods for the compressible Navier-Stokes problem

研究了可压缩线性化Navier-Stokes方程的稳定化有限元方法.对动力方程和连续方程分别应用Galerkin/Petrov最小二乘法和流线扩散法离散,得到一个相容的稳定化有限元格式,证明了此格式在无需满足B-B条件的情况下,解的存在性和唯一性,以及相应的最优误差估计.

A linearized compressible viscous Stokes system is considered. A finite-element formulation is construted by applying Galerkin/Petrov-least squares-type finite methods to momentum equations and streamline diffusion methods to continuity equation. The resulting finite-element formulation is consistent and stable for any combination of discrete velocity and pressure space and uniquely solvable without requiring a Babuska- Brezzi stability condition. An error estimate is obtained.