四川大学学报（自然科学版）2017，Vol.54Issue(2)：231-238,8.DOI:103969/j.issn.0490-6756.2017.03.003
定常Navier-Stokes方程基于速度投影的等阶元稳定化方法
Velocity projection-based stabilized finite element method for steady Navier-Stokes equations using equal order interpolation
摘要
Abstract
A new type of velocity L2 projection-based stabilized finite element method for steady NavierStokes equations is proposed and analyzed.Velocity and pressure are approximated equal order element P1/P1.To overcome the violation of discrete inf-sup condition when equal order elements are used,pressure projection stabilized term is added.Velocity projection-based stabilized method directly increases the L2-stability instead of H1-stability.The main advantage of the proposed methods lies in that,all the computations are performed at the same element level,without the need of nested meshes and the projection of the gradient of velocity.It is showed that this discrete model is stable,given the continuous Navier-Stokes equations has a unique branch of nonsingular solutions.Moreover,error estimates are derived.Numerical experiments show that the method is valid.关键词
定常Navier-Stokes方程/速度L2投影稳定/对流占优/等阶元/压力投影稳定法Key words
Steady Navier-Stokes equation/Velocity L2 projection/Convection-dominated/Equal order element/Pressure projection stabilized method分类
数理科学引用本文复制引用
张百驹,李辉..定常Navier-Stokes方程基于速度投影的等阶元稳定化方法[J].四川大学学报（自然科学版）,2017,54(2):231-238,8.基金项目
国家自然科学基金(11271273) （11271273）
