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  • 1
    Electronic Resource
    Electronic Resource
    Finite element approximation on incompressible Navier-Stokes equations with slip boundary condition (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 697-721 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a mixed finite element approximation of the stationary, incompressible Navier-Stokes equations with slip boundary condition, which plays an important rôle in the simulation of flows with free surfaces and incompressible viscous flows at high angles of attack and high Reynold's numbers. The central point is a saddle-point formulation of the boundary conditions which avoids the well-known Babuška paradox when approximating smooth domains by polyhedrons. We prove that for the new formulation one can use any stable mixed finite element for the Navier-Stokes equations with no-slip boundary condition provided suitable bubble functions on the boundary are added to the velocity space. We obtain optimal error estimates under minimal regularity assumptions for the solution of the continous problem. The techniques apply as well to the more general Navier boundary condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398380
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Mixed finite element approximation of the vector potential (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 685-695 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We consider a mixed finite element approximation of the three dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddlepoint formulation of the essential boundary conditions. In particular, this avoids the wellknown Babuška paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398379
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The stability of finite element methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 93-109 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We give an abstract stability result for finite element methods. It provides a general guideline for establishing the stability of finite element methods for a given norm once it is established with respect to another norm. The abstract result yields stability estimates of natural norms for finite element methods, which have recently been developed to stabilize effects like dominant convection, incompressibility constraints, or boundary conditions. These stability results simplify the error analysis of the discretizations and are helpful fin the convergence analysis of multigrid methods for the solution of the corresponding discrete problems. © 1995 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110108
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  • 4
    Book
    Book
    ¬A¬ review of a posteriori error estimation and adaptive mesh-refinement techniques (1996)
    Chichester u.a. :Wiley-Teubner,
    Details
    Title: ¬A¬ review of a posteriori error estimation and adaptive mesh-refinement techniques
    Author: Verfürth, Rüdiger
    Publisher: Chichester u.a. :Wiley-Teubner,
    Year of publication: 1996
    Pages: 127 S.
    Series Statement: Wiley-Teubner series in advances in numerical mathematics
    Type of Medium: Book
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