Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STABLE LOW ORDER NONCONFORMING QUADRILATERAL FINITE ELEMENTS FOR THE STOKES PROBLEM

  • Published : 2002.05.01
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Abstract

Stability result is obtained for the approximation of the stationary Stokes problem with nonconforming elements proposed by Douglas et al [1] for the velocity and discontinuous piecewise constants for the pressure on qudrilateral elements. Optimal order $H^1$and $L^2$error estimates are derived.

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References

  1. M2AN Math. Model. Numer. Anal. v.33 no.4 Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems J. Douglas, Jr.;J. E. Santos;D. Sheem;X. Ye https://doi.org/10.1051/m2an:1999161
  2. Appl. Math. Comput. v.115 no.2-3 Stacle nonconforming quadrilateral finite elements for the Stokes probles Y. Kim.;S. Lee https://doi.org/10.1016/S0096-3003(99)00145-9
  3. Math. Comp. v.58 no.197 Analysis of locally stabilized mixed finite element methods for the Stokes problem N. Kechkar;D. Silvester https://doi.org/10.2307/2153016
  4. Methods Paritial Differential Equations v.8 Simple nonconforming quadrilateral Stokes element R. Rannacher;S. Turek https://doi.org/10.1002/num.1690080202
  5. Numer. Methods Partial Differential Equations v.11 The Stability of finite element methods R. Verfurth https://doi.org/10.1002/num.1690110108
  6. Math. Comp. v.54 Error analysis of mixed finite element methods for the Stokes problem R. Stenberg https://doi.org/10.2307/2008498
  7. Math. Comp. v.42 no.165 Analysis of mixed finite element methods for the Stokes problem;AA unified approach https://doi.org/10.2307/2007557
  8. Computt. Methods Appl. Mech. Engrg. v.143 The quadrilateral 'Mini' finite element for the Stokes problem W. Bai. https://doi.org/10.1016/S0045-7825(96)01146-2
  9. SIAM J. Numer. Anal. v.34 no.2 Analysis of some quadrilateral nonconforming elements for incompressible elasticity Z. Zhang https://doi.org/10.1137/S0036142995282492