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  • 1985-1989  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Solution of the advective-dispersive transport equation using a least squares collocation, Eulerian-Lagrangian method (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 5 (1989), S. 227-240 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Numerical solution of the advective-dispersive transport equation is difficult when advection dominates. Difficulties arise because of the first-order spatial derivatives which can be elminated by a local coordinate transformation to the characteristic lines of the first order hyperbolic portion of the equation. The resulting differential equation is discretized using a finite difference in time and finite elements in space employing cubic Hermite basis functions. The residuals at individual collocation points are then computed. The sum of the squares of the residuals is minimized to form the necessary set of algebraic equations. The method has performed well in one-dimensional test problems.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690050306
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Least squares collocation solution of differential equations on irregularly shaped domains using orthogonal meshes (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 5 (1989), S. 347-361 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The least squares collocation (LESCO) method has been formulated to solve differential equations defined over irregular domains using a more convenient orthogonal computational mesh. The LESCO method is described in detail for second-order boundary value problems and applied to the time-dependent diffusion and advection-diffusion equations defined over two-dimensional irregular domains. Particular attention is given to the proper procedure for applying boundary conditions. Accuracy, convergence, and consistency are examined. For cubic elements with arbitrary location of collocation points, the convergence rate is between 3rd and 4th order. The major advantages of this method are reduced input data requirements, a more robust procedure for forming the equations, positive definite matrices, and flexibility in distrbuting errors.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690050406
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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