【摘要】 研究了Stokes问题的稳定化有限元方法.对于该问题传统的混合有限元方法求解要求速度和压力的有限元空间组合满足离散的inf-sup条件,为了去掉这一条件的限制,基于非残差的稳定化格式相继被提出,但这些稳定格式都是弱相容的.基于局部投影思想,对Stokes问题提出了一个强相容的稳定化有限元格式,利用有限元空间正交性,证明了此格式在速度和压力有限元空间无需满足B-B条件的情况下,解的存在性和唯一性,并得到了速度和压力相应的误差估计.更多还原

【Abstract】 The Stokes problem is considered.The traditional mixed finite element method requires velocity and pressure finite element spaces combined to meet the discrete inf-sup conditions.In order to overcome the restriction,the stabilized formulation basing on non-residual has been presented,but these formulations are weakly compatible.In this paper a strongly consistent finite element formulation is constructed based on L2 local projection method.It is proved that the finite element formulation is stable and uniquely solvable without requiring a B-B stability condition.An error estimation is obtained.更多还原