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  • 1
    Electronic Resource
    Electronic Resource
    Least squares finite element analysis of laminar boundary layer flows (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 865-876 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the least squares error criterion, a class of finite element is formulated for the numerical analysis of steady state viscous boundary layer flow problems. The method is essentially a discrete element-wise minimization of square and weighted residuals which arise from the attempts in approximately satisfying boundary layer equations. An iterative linearization scheme is developed to circumvent the mathematical difficulties posed by the non-linear boundary layer equations. It results in a process of successive least squares minimizations of residual errors arising from satisfying a set of linear differential equations. A mathematical justification for the method is presented. A major feature of the method lies in the linearization approach which renders non-linear differential equations amenable to linear least squares finite element analysis. Another important feature rests on the proposed finite element formulation which preserves the symmetric nature of finite element matrix equations through the use of the least squares error criterion. Numerical examples of viscous flow along a flat plate are presented to demonstrate the applicability of the method as well as to illuminate discussions on the theoretical aspects of the method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080413
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Efficient least squares finite elements for two-dimensional laminar boundary layer analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 809-825 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the formulations of essentially one-dimensional least squares and Galerkin-least squares finite elements for the numerical solution of two-dimensional laminar boundary layer equations. An iterative technique to cope with the non-linearity of the boundary layer equations, in conjunction with the least squares finite element method, is proposed. Through exhaustive numerical investigations in the retarded flow over a plate, flow past a circular cylinder, the flow past an elliptic cylinder, the accuracy and applicability of the proposed method are demonstrated.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100408
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A least squares finite element approach to unsteady gas dynamics (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1-10 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical technique for solving unsteady gas dynamic equations is presented. The technique is based on least squares finite element concepts with elements that are constructed in both space and time. Both linear and quadratic interpolation is used on individual elements. The technique is tested against a problem whose solution is known so that numerical accuracy can be ascertained.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120102
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Infinite elements with 1/rn type decay (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 347-355 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method of developing a family of 1/rn type infinite elements for the analysis of problems definite in unbounded media. The proposed method is a direct extension of the conventional finite element method. The resulting improper integrals are integrated exactly over the infinite element domains. Two numerical examples in elastic half-space static problems are investigated to illustrate the applicability and accuracy of the method. The use of the proposed infinite elements yields excellent results and preserves all the advantages of the finite element method.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170305
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Convergence of eigenvalue solution in conforming plate bending finite elements (1972)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 4 (1972), S. 217-234 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The convergence proof of plate eigenvalue solution from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem in to a corresponding isoperimetric variational problem. A conforming thick, plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620040208
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Use of the least squares criterion in the finite element formulation (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 75-88 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new method of formulating the finite element relationships based on the least squares criterion. To overcome the high degree of inter-element continuity, a method of reducing the original governing differential equation to a set of equivalent system of first-order differential equations is proposed. The validity of the method is demonstrated by means of several numerical examples. In particular, application of the method to problems with unknown variational functionals is considered.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060109
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Finite elements formulated by the weighted discrete least squares method (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 71-90 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By use of the least squares error criterion, an alternate finite element formulation is presented. The method is based on the discrete or element-wise minimization of square and weighted differential equation residuals which are expressed in terms of element nodal quantities. In order to overcome the stringent inter-element continuity requirement, a major stumbling block, on the element trial functions two practical schemes are proposed. One is the reduction of the original governing differential equation to a system of equivalent first order differential equations; the other is a method of smoothing discontinous trial functions. The latter essentially relaxes the continuity requirement and yields efficient non-conforming finite elements. This paper also demonstrates the use of constant weights which significantly improves the rates of convergence. Several numerical examples illustrate the proposed method. From these examples, it may be concluded that the use of constant weights and the relaxation of the inter-element continuity requirement are two indispensable features of the weighted discrete least square method.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080107
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Transition elements to be used with quarter-point crack-tip elements (1978)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 12 (1978), S. 1031-1036 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalization of the (r-1/2) strain or stress singularity capability of the quadratic isoparametric element is presented. It is shown that, by variable placement of the side-nobe between quarter- and mid-point, the point of singularity sensed by the element can be controlled. By using eight-noded quadrilateral isoparametric elements with appropriately placed side-nodes as transition elements between the quarter-point crack-tip trinagular and remaining non-singular elements, stress intensity factors may be computed with higher accuracy.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620120612
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    Paper (German National Licenses)
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