Abstract
The most frequent motivation for the use of mixed methods is their robustness in the presence of certain limiting and extreme situations. At variance, the main goal of the present paper is to reconsider the use of mixed formulation as a tool for wider application, i.e., to study the stability of the proposed procedure treating problems in elasticity otherwise well suited for the solution by the usual displacement method. Computational procedure for the inf-sup test is outlined, and the results are given.
References
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[2] I. Babuska. On the inf-sup (Babuska-Brezzi) condition. TICAM Forum # 5, 1996.
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[7] M. Berković, Z. Drasković, D. Mijuca. A direct błock sparse solution of the mixed finite element equations. Computer Assisted Mechanics and Engineering Sciences, 5: 21-30, 1998.
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[9] J.H. Bramble, J.E. Pasciak, A.T. Vassilev. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM Numer. Anal., 34, 1997.
[10] F. Brezzi, M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991.
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[12] D. Chapelle, KJ. Bathe. The inf-sup test. Computers and Structures, 47: 537-545, 1993.
[13] F.A. Mirza, M.D. Olson. The mixed finite element in piane elasticity. International Journal of Numerical Methods in Engineering, 15: 273-289, 1980.
[14] O.C. Zienkiewicz, J.Z. Zhu, R.L. Taylor, S. Nakazava. The patch test for mixed formulations. International Journal of Numerical Methods in Engineering, 23: 1873-1883, 1986.
[15] O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method, Vol. I. McGraw-Hill, London, 1989.
[2] I. Babuska. On the inf-sup (Babuska-Brezzi) condition. TICAM Forum # 5, 1996.
[3] M. Berković, Z. Drasković. Stress continuity in the finite element analysis. In: J. Robinson, ed., Accuracy, Reliability and Training in FEM Technology, pp. 110-118. Robinson and Associates, 1984.
[4] M. Berković, Z. Drasković. An efficient solution procedure in mixed finite element analysis. NUMETA 85, pp. 625-633. Balkema, Rotterdam, 1985.
[5] M. Berković, Z. Drasković. On the essential mechanical boundary conditions in two-field finite element approximations. Computer Methods in Applied Mechanics and Engineering, 91: 1339-1355, 1991.
[6] M. Berković, Z. Drasković. A two-field finite element model related to the Reissner's principle. Theoretical and Applied M echanics, 20: 17-36, 1994.
[7] M. Berković, Z. Drasković, D. Mijuca. A direct błock sparse solution of the mixed finite element equations. Computer Assisted Mechanics and Engineering Sciences, 5: 21-30, 1998.
[8] M. Berković, D. Mijuca. An efficient continuous stress mixed model based on the Reissner's principle. Fourth World Congress on Computational Mechanics, Buenos Aires, 1998.
[9] J.H. Bramble, J.E. Pasciak, A.T. Vassilev. Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM Numer. Anal., 34, 1997.
[10] F. Brezzi, M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991.
[11] F. Brezzi, M. Fortin, D. Marini. Mixed finite element methods with continous stresses. Mathematical Models and Methods in Applied Sciences, 3: 275-287, 1993. Springer-Verlag, New York, 1991.
[12] D. Chapelle, KJ. Bathe. The inf-sup test. Computers and Structures, 47: 537-545, 1993.
[13] F.A. Mirza, M.D. Olson. The mixed finite element in piane elasticity. International Journal of Numerical Methods in Engineering, 15: 273-289, 1980.
[14] O.C. Zienkiewicz, J.Z. Zhu, R.L. Taylor, S. Nakazava. The patch test for mixed formulations. International Journal of Numerical Methods in Engineering, 23: 1873-1883, 1986.
[15] O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method, Vol. I. McGraw-Hill, London, 1989.
