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  • 1
    Electronic Resource
    Electronic Resource
    REPLY TO the preceding Discussion by R. G. Thomas of “Applications of Electro-Osmosis to Ground-Water Flow Problems” (1976)
    Oxford, UK : Blackwell Publishing Ltd
    Ground water 14 (1976), S. 0 
    Details
    ISSN: 1745-6584
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1745-6584.1976.tb03112.x
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  • 2
    Electronic Resource
    Electronic Resource
    Applications of Electro-Osmosis to Ground-Water Flow Problems (1975)
    Oxford, UK : Blackwell Publishing Ltd
    Ground water 13 (1975), S. 0 
    Details
    ISSN: 1745-6584
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Geosciences
    Notes: The solution of two-dimensional ground-water flow in soils of low hydraulic conductivity under the influence of both electrokinetic and hydrodynamic forces is found using the finite element method. The example investigated deals with a confined aquifer in which there is a recharging as well as a discharging well present. The results demonstrate the effect of the application of the electro-osmosis phenomenon. The formulation is general and permits the analysis of not only arbitrary shaped boundaries but also different electrode configurations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1745-6584.1975.tb03618.x
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  • 3
    Electronic Resource
    Electronic Resource
    Axisymmetric free surface seepage (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 143-168 
    Details
    ISSN: 0945-3245
    Keywords: MR 35A40 ; MR 39-04 ; MR 65N05 ; ME 65N20 ; MR 16S05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Seepage through porous media in most instances is not a two-dimensional flow phenomenon. One such situation which is investigated herein is the flow from a pond with a bottom formed by the rotation of a curve consisting of a small segment being horizontal and the remainder being an arbitrary convex shaped curve. The approach used to solve this free surface axisymmetric seepage problem is an alternating iteration scheme in conjunction with the Baiocchi transformation and method. The problem is split into two overlapping regions, one in which the free surface is treated and the other in which the singularity is treated. This approach does not require moving meshes and allows a very general prescribed shape for the pond boundary. The numerical approach to the reformulated seepage problem is presented along with several numerical results and comparisons. Also presented is a proof of uniqueness of the solution for such problems provided we make a certain smoothness assumption for the free surface. The alternating iteration scheme is proved to converge provided existence and certain smoothness for the iterates and for their “free surfaces” are assumed. The iterates involved are solutions of certain complementarity systems. The existence and regularity of these solutions is not investigated in this paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400536
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  • 4
    Electronic Resource
    Electronic Resource
    Alternating iteration and elliptic variational inequalities (1985)
    Springer
    Numerische Mathematik 47 (1985), S. 459-481 
    Details
    ISSN: 0945-3245
    Keywords: MR 35A40 ; MR 39-04 ; MR 65N05 ; MR 65N20 ; MR 36S05 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Free boundary value problems, too complicated for formulation as a variational inequality, are broken up into two problems on overlapping regions. On one region the problem is treated as an ordinary boundary value problem; on the second region, the “free boundary part” of the problem is reduced to a variational inequality. By solving the two problems successively it is shown that under certain conditions the successive solutions converge to a single function that gives a solution of the original problem. Application to a filtration problem is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389592
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  • 5
    Electronic Resource
    Electronic Resource
    The dispersion of pollutants beneath open channels (1973)
    Springer
    Water, air & soil pollution 2 (1973), S. 23-34 
    Details
    ISSN: 1573-2932
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract An experiment and a numerical scheme which combine previously given methods for the dispersion and seepage phenomena have been presented to describe the dispersion of a pollutant in porous media beneath a triangular channel. The combined effect of longitudinal and lateral dispersion was considered. Numerical concentration profiles are given along with a comparison of experimental and numerical data. The technique suggested herein can be extended to other channel shapes and flow fields accounting for the capillary fringe.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00572387
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  • 6
    Electronic Resource
    Electronic Resource
    A finite element weighted residual solution to one-dimensional field problems (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 577-585 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The one-dimensional diffusion-convection equation is formulated with the finite element representation employing the Galerkin approach. A linear shape function and two-dimensional triangular and rectangular elements in space and time were used in solving the problem. The results are compared with finite difference solutions as well as the exact solution. As another example, the convective term is set equal to zero and these techniques are applied to the resulting heat equation and similar comparisons are made.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060413
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  • 7
    Electronic Resource
    Electronic Resource
    Transient two-dimensional heat conduction problems solved by the finite element method (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 481-494 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element weighted residual process has been used to solve transient linear and non-linear two-dimensional heat conduction problems. Rectangular prisms in a space-time domain were used as the finite elements. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in tables with analytical, as well as other numerical data. The finite element method compared favourably with these results. It was found to be stable, convergent to the exact solution, easily programmed, and computationally fast. Finally, the method does not require constant parameters over the entire solution domain.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080304
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  • 8
    Electronic Resource
    Electronic Resource
    An application of least squares to one-dimensional transient problems (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 633-647 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of ‘least squares’, which falls under the category of weighted residual processes, is applied as a time-stepping algorithm to one-dimensional transient problems including the heat conduction equation, diffusion-convection equation, and a non-linear unsaturated flow equation. Comparison is made with other time-stepping algorithms, and the least squares method is seen to offer definite advantages.
    Additional Material: 8 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080316
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  • 9
    Electronic Resource
    Electronic Resource
    An investigation of chaos in reaction-diffusion equations (1987)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 3 (1987), S. 139-168 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this article is to investigate graphically and numerically the topic of chaos in reaction-diffusion equations. This article is based on the article by Mitchell and Bruch [1]. One- and two-dimensional forms of the reaction-diffusion equation are discretized using the explicit Euler finite difference scheme. Plots are presented to show the effect of bifurcation parameters on the difference equations. Varying these parameters produce single point, periodic, chaotic, intermittent, and divergent solutions.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690030302
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  • 10
    Electronic Resource
    Electronic Resource
    A numerical solution of an irrigation flowfield (1979)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 3 (1979), S. 23-36 
    Details
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Two-dimensional seepage from an array of triangular channels into permeable soil underlain at a finite depth by a drain has been solved by using the Baiocchi method. The use of this approach allowed a simple formulation of the seepage problem through extension of the solution region to an a priori known region. The new problem was treated numerically by using the S.O.R. method combined with projection. This technique proved to be very accurate when compared with analytical results and efficient from a computer programming standpoint.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nag.1610030104
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