Approximation of the arch problem by residual-free bubbles
A. Agouzal; M. El Alami El Ferricha
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 35, Issue: 2, page 271-293
- ISSN: 0764-583X
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top- D.N. Arnold and R.S. Falk, A uniformly accurate finite element method for the Reissner Mindlin plate. SIAM J. Numer. Anal26 (1989) 1276-1250.
- I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math20 (1973) 179-192.
- I. Babuska and M. Suri, On the locking and robustness in the finite element method. SIAM J. Numer. Anal.29 (1992) 1276-1290.
- C. Baiocchi, F. Brezzi and L. Franca, Virtual bubbles and the Galerkin-Least-squares method. Comput. Methods Appl. Mech. Engrg.105 (1993) 125-141.
- M. Bernadou and Y. Ducatel, Approximation of a general arch problems by straight beam elements. Numer. Math.40 (1982) 1-29.
- F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers. RAIRO-Anal. Numér. (1974) 129-151.
- F. Brezzi and I. Douglas, Stabilized mixed methods for the stokes problem. Numér. Math.53 (1988) 225-236.
- F. Brezzi and M. Fortin, Mixed and hybrid finite Element Methods. Springer-Verlag, Berlin, New-York, Springer Ser. Comput. Math.15 (1991).
- F. Brezzi and A. Russo, Choosing bubbles for advection-diffusion problems. Math. Models Methods Appl. Sci.4 (1994) 571-578.
- B. Budiansky and J.L. Sanders, On the best first order linear shell theory. Progr. Appl. Mech., Mac Millan, New-York, 129-140.
- D. Chenais, Rousselet and B. Benedict, Design sensibivity for arch structures with respect to midsurface shape under static loading. J. Optim. Theory Appl.58 (1988) 225-239.
- D. Chenais and J.-C. Paumier, On the locking phenomenon for a class of elliptic problems. Numer. Math.67 (1994) 427-440
- P.G. Ciarlet, The finite element method for elliptic problems. North Holland, Amsterdam (1978).
- Ph. Destuyender, Some numerical aspects of mixed finite elements for bending plates. Comput. Methods. Appl. Mech. Engrg.78 (1990) 73-87.
- L.P. Franca and T.J.R. Hughes, Two classes of mixed finite element methods. Comput. Methods Appl. Mech. Engrg.69 (1986) 89-129.
- L.P. Franca and A. Russo, Unlocking with residual-free bubbles. Comput. Methods Appl. Mech. Engrg.142 (1997) 361-364
- A. Habbal and D. Chenais, Deterioration of a finite element method for arch structures when thickness goes to zero. Numer. Math.62 (1992) 321-341.
- V. Lods, A new formulation for arch structures. Application to optimization problems. RAIRO-Modél. Math. Anal. Numér.28 (1994) 873-902.
- A.F.D. Loula, L.P. Franca, T.J.R. Hughes and I. Miranda, Stability Convergence and accuracy of a New finite element method for the circular arch problem. Comput. Methods Appl. Mech. Engrg.63 (1987) 281-303.
- Z. Ould Zeidane, Contributions théoriques en Optimisation et Modélisation des structures. Thèse Université de Nice Sophia-Antipolis, Nice (1995).
- A. Russo, Residual-free bubbles and Stabilized methods, in Proc. of the ninth International Conference on finite Elements in Fluids-New Trends and Applications, M.M. Cacchi, K. Morgan, J. Pariaux, B.A. Schreffer, O.C. Zienkiewicz, Eds., Venice (1995) 377-386.
- A. Russo, Bubble Stabilization of finite element methods for the linearized incompressible Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg.132 (1996) 333-343.