Least-Squares Mixed Finite Element Method for a Class of Stokes Equation
-
摘要: 对定常和非定常两种类型的Stokes方程建立了一类新的最小二乘混合元方法,并进行了分析,对定常的方程,采用了对u和σ的不同指标的有限元空间进行计算(LBB条件不需要),得到了最优的H1和L2模估计.对非定常的方程,采用了传统的Raviart-Thomas混合元空间,得到了最优的L2模估计.Abstract: A least-squares mixed finite element method was formulated for a class of Stokes equations in two dimensional domains. The steady state and the time-dependent Stokes' equations were considered. For the stationary equation, optimal L2 and H1 -error estimates are derived under the standard regularity assumption on the finite element partition(the LBB-condition is not required). For the evolutionary equation, optimal L2 estimates are derived under the conventional Raviart-Thomas spaces.
-
Key words:
- Least squares /
- mixed finite element method /
- error estimates
-
[1] Aziz A K,Kellogg R B,Stephens A B.Least-squares methods for elliptic systems[J].Math Comp,1985,44:53~70. [2] Bramble J H,Nitsche J A.A generalized Ritz-least-squares method for Dirichlet problems[J].SIAM J Numer Anal,1973,10:81~93. [3] Raviart R A,Thomas J M.A mixed finite element method for 2nd elliptic problems[A].In:Math Aspects of the FEM,Lecture Notes in Math[C].Vol,606,Berlin and New York:Springer-Verlag,1977,292~315. [4] Brezzi F.On the existence,uniqueness and approximation of saddle point problems arising from Lagrange multipliers[J].RAIRO Anal Numer,1974,8:129~151. [5] Carey G F,Oden J T.Finite Element:A Second Course[M].VolⅡ.Englewood Cliffs N J:Printice-Hall,1983. [6] Pehlivanov A I,Carey G F,Lazarov R D.Least-squares mixed finite element for second-order elliptic problems[J].SIAM J Numer Anal,1994,5:1368~1377. [7] Pehlivanov A I,Carey G F.Error estimates for least-squares mixed finite elements[J].Math Model Numer Anal,1994,5:517~537. [8] Cai Z,Lazarov R,Nanteuffel T A,et al.First-order system least squares for second-order partial differential equations Part Ⅰ[J].SIAM J Numer Anal,1994,6:1785~1799. [9] Johnson C,Thomee V.Error estimates for some mixed finite element methods for parabolic type problems[J].RAIRO Anal Numer,1981,15:41~78. [10] Girault V,Raviart P A.Finite element approximation of the Naviart-Stokes equations[A].In:Lecture Notes in Mathematics[C].Vol 749,Berlin,Heidelberg,New York:Springer-Verlag,1979. [11] Wheeler M F.A priorierror estimates for Galerkin approximations to parabolic partial differential equations[J].SIAM J Numer Anal,1973,4:723~758.
点击查看大图
计量
- 文章访问数: 1972
- HTML全文浏览量: 57
- PDF下载量: 732
- 被引次数: 0