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  • 1
    Electronic Resource
    Electronic Resource
    An unconditionally stable implicit method for hyperbolic conservation laws (1985)
    Springer
    Journal of engineering mathematics 19 (1985), S. 33-44 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary We construct a space-centered self-adjusting hybrid difference method for one-dimensional hyperbolic conservation laws. The method is linearly implicit and combines a newly developed minimum dispersion scheme of the first order with the recently developed second-order scheme of Lerat. The resulting method is unconditionally stable and unconditionally diagonally dominant in the linearized sense. The method has been developed for quasi-stationary problems, in which shocks play a dominant role. Numerical results for the unsteady Euler equations are presented. It is shown that the method is non-oscillatory, robust and accurate in several cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00055039
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  • 2
    Electronic Resource
    Electronic Resource
    On the accuracy of least-squares finite elements for a first-order conservation equation (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 957-964 
    Details
    ISSN: 0271-2091
    Keywords: Conservation equation ; Hyperbolic equation ; Least squares ; Finite elements ; 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: The numerical solution of a single first-order conservation equation by a least-squares finite element method is considered. Isoparametric bilinear quadrilateral elements are used. The accuracy is studied numerically and it is shown that the discrete equations associated with nodal points on the boundaries should be modified in order to obtain an accurate numerical solution.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080807
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Improving the accuracy of the least-squares finite element approximation of the linearized steady Euler equations by an embedding method (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 977-987 
    Details
    ISSN: 0271-2091
    Keywords: Euler equations ; Least squares ; Finite elements ; Embedding methods ; 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: The standard least-squares finite element method for the linearized Euler equations turns out to be inaccurate. This method is studied in detail for a system of composite type, obtained by transformation of the linearized Euler equations. The shortcomings of the method are clarified and an embedding method is constructed. It is shown numerically that this new method is O(h2)-accurate.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080809
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A fully implicit splitting method for accurate tidal computations (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2707-2721 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Often industrial codes for the numerical integration of the 2D shallow water equations are based on an Alternating Direction Implicit method. However, for large time steps these codes suffer from inaccuracies when dealing with a complex geometry or bathymetry. This reduces the performance considerably. In this paper a new method is presented in which these inaccuracies are absent, even for large time steps. The method is a fully implicit time integration method. In order to obtain linear systems that can be solved efficiently, we introduce a time splitting method. The resulting linear systems are solved iteratively by using the preconditioned Conjugate Gradients Squared method.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261209
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    Paper (German National Licenses)
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