期刊文献+

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem 被引量:6

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem
原文传递
导出
摘要 We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)- conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element. We consider a singular perturbation problem which describes 2D Darcy-Stokes flow.An H(div)-conforming rectangular element,DS-R14,is proposed and analyzed frst.This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant.We then simplify this element to get another H(div)-conforming rectangular element,DS-R12,which has 12 degrees of freedom for velocity.The uniform convergence is also obtained for this element.Finally,we construct a de Rham complex corresponding to DS-R12 element.
出处 《Science China Mathematics》 SCIE 2013年第12期2723-2736,共14页 中国科学:数学(英文版)
基金 supported by National Natural Science Foundation of China(Grant No.11071226) the Hong Kong Research Grants Council(Grant No.201112)
关键词 Darcy-Stokes problem H(div)-conforming rectangular elements uniform convergence Stokes问题 一致收敛 元素 矩形 生日 奇异摄动问题 4自由度 2自由度
  • 相关文献

参考文献3

二级参考文献42

  • 1L.P. Franca and T.J.R. Hughes, Two classes of finite element methods, Comput. Method. Appl. M., 69 (1988), 89 -129.
  • 2J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev., 34 (1992), 581- 613.
  • 3V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms., Springer-Verlag, 1986.
  • 4F. Brezzi, On the existence, uniqueness and approximation of saddle point problems arising from Lagrange multipliers, RAIRO Numer. Anal., 8 (1974), 129 -151.
  • 5F. Brezzi and M. Fortin, Mixed and hybrid finite element methods, Springer Series in Computational Mathematics 15, Springer-Verlag, 1991.
  • 6M.A. Olshanskii and A. Reusken, Analysis of a Stokes interface problem, Numer. Math., 103 (2006), 129-149.
  • 7P.M. Crouzeix and P.A. Raviart, Conforming and nonconforming finite element methods for solving the stationary Stokes equations I, RAIRO, 76 (1973), 3- 33.
  • 8L.R. Scott and M. Vogelius, Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials, Math. Mod. Num. Anal., 19 (1985), 111- 143.
  • 9D.N. Arnold and J. Qin, Quadratic velocity/linear pressure stokes elements, Advances in Computer Methods for Partial Differential Equations-VII IMACS, (1992), 28- 34.
  • 10J. Qin, On the Convergence of Some Low Order Mixed Finite Elements for Incompressible Fluids, Ph.D. Thesis, Penn State University, Department of Mathematics, (1994).

共引文献29

同被引文献6

引证文献6

二级引证文献12

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部