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  • 1
    ISSN: 1433-0369
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Here we point out some difficulties arising in the approximation of the vibration frequencies of a fluid in a cavity in the case of non convex polygonal domains. Since the eigensolutions must satisfy an irrotationality condition, a classical way to face the problem is to consider a penalized formulation. Unfortunately standard conforming finite elements fail to give good results. We intend to justify this failure and to suggest a finite element method based on a reduced integration strategy able to give reasonable results.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the Stokes problem by using a mixed finite element method introduced by Stenberg [Numer. Math. 56, 827 (1990)] and adapt it to the splitting introduced by Canuto and Sacchi Landriani [Numer. Math. 50, 217 (1986)] and Chinosi and Comodi [Numer. Methods Partial Different. Equations 7, 363 (1991)], by using the incompressibility condition to implicitly define a boundary condition for the pressure. © 1994 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    ISSN: 1069-8299
    Keywords: shell problem ; Naghdi model ; finite elements ; mixed elements ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness. Copyright © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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