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  • 1
    Electronic Resource
    Electronic Resource
    On the approximation of the unsteady Navier–Stokes equations by finite element projection methods (1998)
    Springer
    Numerische Mathematik 80 (1998), S. 207-238 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):35Q30, 65M12, 65M60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. This paper provides an analysis of a fractional-step projection method to compute incompressible viscous flows by means of finite element approximations. The analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method. Such a theoretical distinction leads to a finite element projection method with a Poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm. Error estimates in finite time are given. An extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050366
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Simulation of 2D External Viscous Flows by Means of a Domain Decomposition Method
    Amsterdam : Elsevier
    Journal of Computational Physics 108 (1993), S. 343-352 
    Details
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/jcph.1993.1187
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  • 3
    Electronic Resource
    Electronic Resource
    Subgrid stabilization of Galerkin approximations of linear contraction semi-groups of class C0 (1999)
    Springer
    Computing and visualization in science 2 (1999), S. 131-138 
    Details
    ISSN: 1433-0369
    Keywords: Key words: Finite Elements – Galerkin methods – Stabilization – Linear hyperbolic equations – Semi-groups – Subgrid modeling – Artificial viscosity – Multi-scale methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. This paper presents a stabilized Galerkin technique for approximating linear contraction semi-groups of class C0 in a Hilbert space. The main result of this paper is that this technique yields optimal error estimates in the graph norm. The key idea is twofold, first it consists in introducing an approximation space that is broken up into resolved scales and subgrid scales so that the generator of the semi-group satisfies a uniform inf-sup condition with respect to this decomposition. Second, the Galerkin approximation is slightly modified by introducing an artificial diffusion acting only on the subgrid scales.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007910050035
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Equivalence of u-p and ζ-ψ formulations of the time-dependent Navier-Stokes equations (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 471-487 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible flows ; Navier-Stokes equations ; Primitive variables ; Vorticity-Streamfunction ; Compatibility conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper deals with the non-stationary incompressible Navier--Stokes equations for two-dimensional flows expressed in terms of the velocity and pressure and of the vorticity and streamfunction. The equivalence of the two formulations is demonstrated, both formally and rigorously, by virtue of a condition of compatibility between the boundary and initial values of the normal component of velocity. This condition is shown to be the only compatibility condition necessary to allow for solutions of a minimal regularity, namely H1 for the velocity, as in most current numerical schemes relying on spatial discretizations of local type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650180504
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  • 5
    Electronic Resource
    Electronic Resource
    On stability and convergence of projection methods based on pressure Poisson equation (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1039-1053 
    Details
    ISSN: 0271-2091
    Keywords: incompressible Navier-Stokes equations ; projection method ; fractional-step method ; pressure Poisson equation ; finite elements ; stabilization methods ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This work investigates the proper choices of spatial approximations for velocity and pressure in fractional-step projection methods. Numerical results obtained with classical finite element interpolations are presented. These tests confirm the role of the inf-sup LBB condition in non-incremental and incremental versions of the method for computing viscous incompressible flows. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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