First-order system least squares for linear elasticity: numerical results

SIAM Journal of Scientific Computing

Volumn 21, Issue 5, 2000, Pages 1706-1727

  Cai, Z ^a   Lee, C O ^b   Manteuffel, T A ^c   Mccormick, S F ^c  

^a PURDUE UNIVERSITY   (United States)

^b Inha University   (South Korea)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; TENSORS; VECTORS;

FIRST ORDER SYSTEM LEAST SQUARES; LAME CONSTANTS; LINEAR ELASTICITY; PURE DISPLACEMENT PROBLEM; PURE TRACTION PROBLEM; STRAIN TENSOR; STRESS TENSOR;

LEAST SQUARES APPROXIMATIONS;

EID: 0033709989     PISSN: 10648275     EISSN: None     Source Type: None    
DOI: 10.1137/S1064827598338640     Document Type: Article

References (15)

1. I. BABUŠKA AND B. SZABO, On the rates of convergence of the finite element method, Internat. J. Numer. Methods Engrg., 18 (1982), pp. 323-341.
2. S. C. BRENNER, A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity, Math. Comp., 63 (1994), pp. 435-460, S1-S5.
3. S. C. BRENNER, Multigrid methods for parameter dependent problems, RAIRO Modél. Math. Anal. Numér, 54 (1996), pp. 265-297.
4. S. C. BRENNER AND L. Y. SUNG, Linear finite element methods for planar linear elasticity, Math. Comp, 59 (1992), pp. 321-338.
5. W. L. BRIGGS, V. E. HENSON, AND S. F. MCCORMICK, A Multigrid Tutorial, 2nd ed., SIAM, Philadelphia, 2000, to appear.
6. Z. CAI, C.-O. LEE, T. A. MANTEUFFEL, AND S. F. MCCORMICK, First-order system least squares for the Stokes and linear elasticity equations: Further results, SIAM J. Sci. Comput., 21 (2000), pp. 1728-1739.
7. Z. CAI, T. A. MANTEUFFEL, AND S. F. MCCORMICK, First-order system least squares for the Stokes equations, with application to linear elasticity, SIAM J. Numer. Anal., 34 (1997), pp. 1727-1741.
8. Z. CAI, T. A. MANTEUFFEL, S. F. MCCORMICK, AND S. PARTER, First-order system least squares (FOSLS) for planar linear elasticity: pure traction problem, SIAM J. Numer. Anal., 35 (1998), pp. 320-335.
9. C. L. CHANG, A least-squares finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 83 (1990), pp. 1-7.
10. P. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
11. J. DOUGLAS AND J. WANG, An absolutely stabilized finite element method for the Stokes problem, Math. Comp., 52 (1989), pp. 495-508.
12. C.-O. LEE, A conforming mixed finite element method for the pure traction problem of linear elasticity, Appl. Math. Comp., 93 (1998), pp. 11-29.
13. P. PODIO-GUIDUGLI AND G. VERGARA-CAFFARELLI, On a class of live traction problems in elasticity, in Trends and Applications of Pure Mathematics to Mechanics, P. Ciarlet and M. Roseau, eds., Lecture Notes in Phys., Springer, Berlin, New York, 1995, pp. 291-304.
14. R. STENBERG, A family of mixed finite elements for the elasticity problem, Numer. Math., 53 (1988), pp. 513-538.
15. M. VOGELIUS, An analysis of the p-version of the finite element method for nearly incompressible materials: uniformly valid, optimal error estimates, Numer. Math., 41 (1983), pp. 39-53.