A Galerkin/least-square finite element formulation for nearly incompressible elasticity/stokes flow

Applied Mathematical Modelling

Volumn 31, Issue 3, 2007, Pages 513-529

  Xia, Kaiming ^a   Yao, Haishen ^b  

^a 1120 Science and Engineering Offices   (United States)

^b CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

Galerkin least square; Incompressible elasticity stokes flow; Second derivatives of shape functions; Stabilized term

Indexed keywords

ELASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS;

GALERKIN/LEAST-SQUARE; SECOND DERIVATIVE; SHAPE FUNCTION; STABILIZED TERM; STOKES FLOW;

INCOMPRESSIBLE FLOW;

ELASTICITY; FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW;

EID: 33750823705     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2005.11.009     Document Type: Article

References (11)

1. Babuska I. The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179-192
2. Hughes T.J.R., Franca L.P., and Balestra M.A. A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. Comput. Meth. Appl. Mech. Eng. 59 (1986) 85-99
3. Ozienkiewicz O.C., and Taylor R.L. The Finite Element Method, vol. 1. fourth ed. (1994), McGraw Hill, New York
4. Hughes T.J.R., Franca L.P., and Balestra M.A. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least square methods for advective-diffusive equations. Comput. Meth. Appl. Mech. Eng. 73 (1989) 173-189
5. Brezzi F., Bristeau M.O., Franca L., Mallet M., and Roge G. A relationship between stabilized finite element methods and the Galerkin method with bubble functions. Comput. Meth. Appl. Mech. Eng. 96 (1992) 117-129
6. Baiocchi C., Brezzi F., and Franca L. Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S). Comput. Meth. Appl. Mech. Eng. 105 (1993) 125-141
7. Onate E. Derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems. Comput. Meth. Appl. Mech. Eng. 151 (1998) 233-265
8. Klaas O., Maniatty A., and Shephard M. A stabilized mixed finite element method for finite elasticity. Formulation for linear displacement and pressure interpolation. Comput. Meth. Appl. Mech. Eng. 180 (1999) 65-79
9. Maniatty A., Liu Y., Klass O., and Shephard M.S. Higher order stabilized finite element method for hyperelastic finite deformation. Comput. Meth. Appl. Mech. Eng. 191 (2002) 1491-1503
10. Commend S., Truty A., and Zimmermann T. Stabilized finite elements applied to elastoplasticity: I. Mixed displacement-pressure formulation. Comput. Meth. Appl. Mech. Eng. 193 (2003) 3559-3586
11. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987), Prentice-Hall, Englewoods Cliffs, NJ