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  • Numerical Methods  (4)
  • finite elements  (4)
  • 1
    Electronic Resource
    Electronic Resource
    AN ADAPTIVE FINITE ELEMENT SCHEME FOR HYDRAULIC FRACTURING WITH PROPPANT TRANSPORT (1997)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 24 (1997), S. 645-670 
    Details
    ISSN: 0271-2091
    Keywords: hydraulic fracturing ; finite elements ; moving adaptive grids ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A mathematical model and adaptive finite element scheme are developed for describing the distribution of proppant in a propagating hydraulic fracture. The governing equation for proppant concentration is derived by applying the conservation law of mass to the proppant and to the proppant-laden fluid. Shah's empirical equation, which relates the proppant concentration and the indices of the non-Newtonian fluid, is used to describe the proppant-laden fluid. The proppant distribution inside a hydraulic fracture can then be obtained by solving the proppant concentration equation together with the governing equations of fluid and elasticity for a hydraulic fracturing. A novel moving grid scheme is developed that combines grid point insertion with redistribution. Four examples corresponding to different in situ stress distributions are computed to demonstrate the scheme. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 2
    Electronic Resource
    Electronic Resource
    FINITE ELEMENT ANALYSIS OF ANISOTROPIC FLUID SUSPENSIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 11-27 
    Details
    ISSN: 0271-2091
    Keywords: finite elements ; liquid crystal ; nematic ; anisotropic ; electro rheological ; 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 orientation tensor L is introduced to construct a modified Leslie-Ericksen model for the viscous, incompressible flow of anisotropic suspensions (including electric field effects). This is then utilized to develop a weak variational formulation and finite element scheme for computing the flow and orientation fields. Numerical results are presented for exploratory test problems.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    AN ENTROPY VARIABLE FORMULATION AND APPLICATIONS FOR THE TWO-DIMENSIONAL SHALLOW WATER EQUATIONS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 29-46 
    Details
    ISSN: 0271-2091
    Keywords: shallow water equations ; entropy variables ; streamline upwind Petrov-Galerkin ; symmetric formulations ; 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: A new symmetric formulation of the two-dimensional shallow water equations and a streamline upwind Petrov-Galerkin (SUPG) scheme are developed and tested. The symmetric formulation is constructed by means of a transformation of dependent variables derived from the relation for the total energy of the water column. This symmetric form is well suited to the SUPG approach as seen in analogous treatments of gas dynamics problems based on entropy variables. Particulars related to the construction of the upwind test functions and an appropriate discontinuity-capturing operator are included. A formal extension to the viscous, dissipative problem and a stability analysis are also presented. Numerical results for shallow water flow in a channel with (a) a step transition, (b) a curved wall transition and (c) a straight wall transition are compared with experimental and other computational results from the literature.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Least-squares finite elements for fluid flow and transport (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 97-107 
    Details
    ISSN: 0271-2091
    Keywords: least-squares ; finite elements ; flow ; transport ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The least-squares mixed finite element method is concisely described and supporting error estimates and computational results for linear elliptic (steady diffusion) problems are briefly summarized. The extension to the stationary Navier-Stokes problems for Newtonian, generalized Newtonian and viscoelastic fluids is then considered. Results of numerical studies are presented for the driven cavity problem and for a stick-slip problem. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 5
    Electronic Resource
    Electronic Resource
    Natural and postprocessed superconvergence in semilinear problems (1991)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 7 (1991), S. 245-259 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence error estimates are established for a class of semilinear problems defined by a linear elliptic operator with a nonlinear forcing term. The analysis is for rectangular biquadratic elements, and we prove superconvergence of the derivative components along associated lines through the Gauss points. Derivative postprocessing formula and formulas for integrals are also considered and similar superconvergence estimates proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690070304
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  • 6
    Electronic Resource
    Electronic Resource
    Least-squares finite element approximation of Fisher's reaction-diffusion equation (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 175-186 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Fisher's equation is a classical diffusion-reaction type of problem describing diffusion and nonlinear reproduction of a species. In the present study we develop a least-squares finite element formulation of Fisher's equation and carry out supporting numerical studies. Of particular interest are questions associated with the approximation of progressive wave solutions with minimum speed and the viability of the least-squares approach for this class of problem. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110206
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A regularization-stabilization technique for nonlinear conservation equation computations (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 4 (1988), S. 165-171 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A regularization procedure for nonlinear conservation equations is introduced and demonstrated to have a stabilizing effect on the numerical solution of the associated approximate problem. Representative results for a least-squares finite-element method are given, and the numerical performance of the stabilization procedure explored. The effect of the regularization term is similar to a local numerical dissipation dependent on the numerical itegration time step.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690040302
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  • 8
    Electronic Resource
    Electronic Resource
    Superconvergence phenomena in nonlinear two-point boundary-value problems (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 561-577 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Superconvergence estimates are derived for a class of strongly nonlinear two-point boundary-value problems. The analysis considers solution and gradient superconvergence points as well as flux postprocessing formulas. Finally, the extension to parabolic problems is considered. © 1993 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090506
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    Paper (German National Licenses)
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