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  • 1
    Electronic Resource
    Electronic Resource
    Iterative solution of the stream function-vorticity equations using a multigrid solver with finite elements (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 587-594 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The solution of the stream function-vorticity equations is developed using a multigrid method to improve efficiency in a finite-element p-method. The equations are discretized using 2-D Lagrange finite elements (linear, quadratic and cubic) and solved in iteratively decoupled form using successive approximation and continuation methods. The comparative performance of several multigrid and direct matrix solvers is investigated with respect to convergence characteristics and time performance on the Cray Y-MP.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090706
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Editorial preface for the second decade of Communications in Numerical Methods in Engineering (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. iii 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110102
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  • 3
    Electronic Resource
    Electronic Resource
    Some conformal map constructs for numerical grids (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 127-135 
    Details
    ISSN: 1069-8299
    Keywords: conformal mapping ; numerical grids ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop some special conformal maps and related strategies for grid generation in certain ‘difficult’ domains. Of particular interest are non-convex domains, and domains with corners and cusps.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110206
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  • 4
    Electronic Resource
    Electronic Resource
    Stream function vorticity solution using high-p element-by-element techniques (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 387-395 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A p-type finite-element scheme is introduced for Navier-Stokes problems in a fully coupled stream function/vorticity formulation. The resulting coupled non-linear system is solved using a Newton iteration with incremental continuation in the Reynold's number. A biconjugate gradient (BCG) scheme in an element-by-element setting is applied to solve the linearized system at each Newton iteration. Pseudo-element block preconditioners produce a practical PBCG method, even for ill-conditioned systems arising from high-p elements in the case of Stokes flow. The problem at higher Reynolds numbers further limits p.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090504
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  • 5
    Electronic Resource
    Electronic Resource
    A note on Richardson extrapolation as an error estimator for non-linear reaction-diffusion problems (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 533-540 
    Details
    ISSN: 1069-8299
    Keywords: extrapolation ; non-linear potential equation ; reaction-diffusion ; semiconductors ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop and test a 6th-order Richardson extrapolation scheme as an error estimator for reaction-diffusion problems. Supporting numerical experiments are presented. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 6
    Electronic Resource
    Electronic Resource
    Higher-order compact mixed methods (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 553-564 
    Details
    ISSN: 1069-8299
    Keywords: mixed methods ; high-order finite differences ; compact stencils ; superconvergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We develop a class of higher-order mixed finite difference methods for elliptic partial differential equations. The problem is recast as a first-order mixed system and the higher-order compact schemes follow as a natural extension of the formulations we developed previously for the scalar PDE problem. Since the flux appears explicitly in the mixed formulation we obtain higher-order (nodal superconvergent) solutions in both the primary solution field and also the flux. Some supporting numerical experiments are included to demonstrate the superconvergent rates. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 7
    Electronic Resource
    Electronic Resource
    A class of data structures for 2-D and 3-D adaptive mesh refinement (1988)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 26 (1988), S. 2607-2622 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A ‘family’ of tree data structures for adaptive mesh refinement is described and details concerning the associated logic are provided. The data structures encompass triangular elements and quadrilateral elements in two dimensions and quadrilateral bricks in three dimensions. Furthermore, both linear (bilinear) and quadratic (biquadratic) element types, respectively, are developed. Representative refinement results are given for the bilinear, trilinear and biquadratic types and associated performance studies made for the refinement procedure.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620261203
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  • 8
    Electronic Resource
    Electronic Resource
    Superconvergent derivatives: A Taylor series analysis (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 489-509 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An analysis, based on the use of Taylor series expansions, is developed to determine accuracy estimates for derivatives in one and two dimensions computed by differentiation of a finite-element interpolant or approximation. The analysis clarifies some issues concerning special points at which the derivatives are believed to be exceptionally accurate with higher convergence rates (superconvergence). Moreover, it leads directly to a class of post-processing strategies for the derivatives and offers a more direct constructive approach to the subject.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280302
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  • 9
    Electronic Resource
    Electronic Resource
    Viscous flow and transport with moving free and reactive surfaces (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1181-1194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Transport of a chemical species through a viscous fluid with reaction at an interface is modelled by a quasi-static process in which the transient behaviour is dominated by motion of the reactive surface. The reaction is accompanied by a molar volume change which leads to motion of the free surface. A decoupled stream function-vorticity formulation is introduced in conjunction with a moving finite element method. This also permits convenient treatment of the free and reactive surface boundary conditions. The model is applied to the growth of oxide films on silicon surfaces and reveals the effect of surface curvature on film growth.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300607
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  • 10
    Electronic Resource
    Electronic Resource
    A perturbation analysis and finite element approximate model for free surface flow over curved beds (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 493-507 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A perturbation analysis is developed for 1-D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non-linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep-slope shallow water formulation corresponding to the model with zero curvature.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310306
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