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  • Mathematics and Statistics  (5)
  • Finite elements  (3)
  • 1
    Electronic Resource
    Electronic Resource
    Coupled heat transfer and viscous flow, and magnetic effects in weld pool analysis (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 713-730 
    Details
    ISSN: 0271-2091
    Keywords: Viscous flow ; Heat transfer ; Phase change ; Finite elements ; Magnetic field ; 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 finite element formulation and analysis is developed to study coupled heat transfer and viscous flow in a weld pool. The thermal effects generate not only buoyancy forces but also a variation in the surface tension which acts to drive the viscous flow in the molten weld pool. A moving phase boundary separates molten and solid material. Numerical experiments reveal the nature of the highly convective flow in the weld pool and the associated thermal profiles. The relative importance of buoyancy, surface tension, phase change, convection, etc. are examined. We also consider the sensitivity of the solution to the finite element mesh and related non-linear numerical instabilities. Of particular interest is the coupling of the thermal and viscous flow fields for the case when radial flow is inward or outward.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090605
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Periodic viscous flow: A bench-mark problem (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 87-97 
    Details
    ISSN: 0271-2091
    Keywords: Periodic ; Unsteady ; Viscous flow ; 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 double-transform technique provides a semi-analytic solution in the form of a series expansion for unsteady axisymmetric Stokes flow in the entrance region of a semi-infinite rigid cylindrical tube. This in turn offers an appropriate bench-mark problem for evaluating the quality of numerical approximations. To illustrate this, periodic axial flow in a circular cylinder is considered. Some aspects of the bench-mark problem that are of interest include the reverse flow in the wall layers, the accuracy of the approximate method in different flow regimes and the mesh grading. This bench-mark problem and the numerical study provide some insight into practical issues pertinent to the approximate solution of unsteady and periodic flows.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110106
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A least squares finite element method for viscoelastic fluid flow problems (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 943-953 
    Details
    ISSN: 0271-2091
    Keywords: Viscoelastic ; 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: Viscoelastic flows remain a demanding class of problems for approximate analysis, particularly at increasing Weissenberg numbers. Part of the difficulty stems from the convective behavior and in the treatment of the stress field as a primary unknown. This latter aspect has led to the use of higher-order piecewise approximations for the stress approximation spaces in recent finite element research. The computational complexity of the discretized problem is increased significantly by this approach but at present it appears the most viable technique for solving these problems. Motivated by recent success in treating mixed systems and convective problems, we formulate here a least squares finite element method for the viscoelastic flow problem. Numerical experiments are conducted to test the method and examine its strengths and limitations. Some difficulties and open issues are identified through the numerical experiments. We consider the use of high degree elements (p refinement) to improve performance and accuracy.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650171103
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    Paper (German National Licenses)
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  • 4
    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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    Paper (German National Licenses)
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  • 5
    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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  • 6
    Electronic Resource
    Electronic Resource
    A high-order compact formulation for the 3D Poisson equation (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 235-243 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work we construct an extension to a class of higher-order compact methods for the three-dimensional Poisson equation. A superconvergent nodal rate of O(h6) is predicted, or O(h4) if the forcing function derivatives are not known exactly. Numerical experiments are conducted to verify these theoretical rates. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 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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