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  • 1
    Electronic Resource
    Electronic Resource
    A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations (1999)
    Springer
    Calcolo 36 (1999), S. 215-232 
    Details
    ISSN: 1126-5434
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract: Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component of the velocity in the stationary Stokes and Navier–Stokes equations, along with a piecewise-constant element for the pressure. We obtain a stable element in both cases for which optimal error estimates for the approximation of both the velocity and pressure in L 2 can be established, as well as one in a broken H 1-norm for the velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100920050031
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stabilized finite element approximations for the Reissner–Mindlin plate (2000)
    Springer
    Advances in computational mathematics 13 (2000), S. 375-386 
    Details
    ISSN: 1572-9044
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Based on the Helmholtz decomposition of the transverse shear strain, Brezzi and Fortin in [5] introduced a three-stage algorithm for approximating the Reissner–Mindlin plate model with clamped boundary conditions and established uniform error estimates in the plate thickness. The first- and third-stage involve approximating two simple Poisson equations and the second-stage approximating a perturbed Stokes equation. Instead of using the mixed finite element method which is subject to the inf–sup condition, we consider a stabilized finite element approximation to such perturbed Stokes equations. Optimal error estimates independent of thickness of the plate are obtained for such equations. Then error analysis is established for the whole system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1016693613626
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  • 3
    Electronic Resource
    Electronic Resource
    A discrete divergence-free basis for finite element methods (1997)
    Springer
    Numerical algorithms 16 (1997), S. 365-380 
    Details
    ISSN: 1572-9265
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The divergence-free finite element method (DFFEM) is a method to find an approximate solution of the Navier–Stokes equations in a divergence-free space. That is, the continuity equation is satisfied a priori. DFFEM eliminates the pressure from the calculations and significantly reduces the dimension of the system to be solved at each time step. For the standard 9-node velocity and 4-node pressure DFFEM, a basis for the weakly divergence-free subspace is constructed such that each basis function has nonzero support on at most 4 contiguous elements. Given this basis, weakly divergence-free macroelements are constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019159702198
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    The construction of an optimal weakly divergence-free macroelement (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2245-2262 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The divergence-free finite element method (DFFEM) is a method to find an approximate solution of the Navier-Stokes equations in a divergence-free space. That is, the continuity equation is satisfied a priori. DFFEM eliminates the pressure from the calculations and reduces significantly the dimension of the system to be solved at each time step. For the standard 8-node velocity and 4-node pressure DFFEM, an optimal basis for the weakly divergence-free subspace is constructed such that each basis function has non-zero support on at most nine contiguous elements. Given this basis, weakly divergence-free macroelements are constructed.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361307
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    Paper (German National Licenses)
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