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  • 1985-1989  (12)
  • 1989  (7)
  • 1987  (5)
  • 1
    Electronic Resource
    Electronic Resource
    Determination of interfacial stress during thermal oxidation of silicon (1989)
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 65 (1989), S. 3667-3670 
    Details
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We develop a theoretical model to obtain the stress in oxide films occurring during thermal oxidation of silicon. The model results in a prediction of 4.5×109 dyn/cm2 for the interfacial stress, in excellent agreement with laboratory measurements. Moreover, we establish generally that the interfacial stress is proportional to 1−γ, where γ is the molar volume ratio of reactant to product. For silicon oxidation, γ=4/9, and the resulting stress is compressive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.342592
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Basis function selection and preconditioning high degree finite element and spectral methods (1989)
    Springer
    BIT 29 (1989), S. 794-804 
    Details
    ISSN: 1572-9125
    Keywords: AMS 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This work considers the effect of the choice of finite element basis on the conditioning and iterative solution of the algebraic systems obtained using high degree finite elements (p-methods). This issue is fundamental to the performance ofp-methods and to the increased use of iterative solution techniques both for standard finite element analysis and also in adaptivep solutions. The central ideas also apply to high degree spectral methods (global expansion methods).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01932746
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Treatment of material discontinuities in finite element computations (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 393-417 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider finite element analysis of problems with discontinuous material coefficients. For applications in which the material interface crosses an element, we develop special elements with an embedded flux constraint at the interface. This new procedure is compared with the standard finite element method with interface coincident with the element boundary and with an existing method proposed by Steven.1 Supporting numerical studies are conducted and rates of convergence for the solution and interface flux are examined. Some local superconvergence behaviour is observed.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240209
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Least-squares finite element method and preconditioned conjugate gradient solution (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 1283-1296 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least-squares variational procedure for first-order systems of differential equations and an approximate formulation based on finite elements are developed. Error estimates, a condition number bound and analysis of weighting factors are given. Steepest descent and conjugate gradient solution procedures are examined, and an appropriate preconditioner constructed which is demonstrated to yield rapid convergence and to be insensitive to problem size. Numerical studies of rates of convergence for a test problem are given.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240705
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  • 5
    Electronic Resource
    Electronic Resource
    Adaptive mesh redistribution for a boundary element (panel) method (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 2315-2325 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, we extend the concept of a grading function, as introduced by Carey and Dinh2 in a one-dimensional context, to curved contours. We then apply the idea to adaptive grid redistribution for a boundary element method to solve a model boundary value problem. Numerical results are included for a potential problem to demonstrate the effect of the redistribution scheme on the solution and the geometry of the domain.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620241206
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  • 6
    Electronic Resource
    Electronic Resource
    Adaptive refinement for least-squares finite elements with element-by-element conjugate gradient solution (1987)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 24 (1987), S. 569-580 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An error analysis and an adaptive refinement scheme are developed for use with a class of least-squares finite element methods. The error indicators for the refinement procedure are based on element residuals which are calculated as part of the least-squares method. The solution scheme used in the supporting numerical studies employs an elment-by-element conjugate gradient algorithm. Consequently, storage and computation are not influenced by nodal numbering.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620240308
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  • 7
    Electronic Resource
    Electronic Resource
    Stream function solution of Navier-Stokes problems with inter-element penalties (1987)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 7 (1987), S. 191-193 
    Details
    ISSN: 0271-2091
    Keywords: Finite Elements ; Interface Penalties ; Viscous Flow ; 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: In this note, we apply a finite element stream function formulation with inter-element penalties to the Navier-Stokes equations. The approach is an extension of a technique previously introduced for Stokes, flow. The solution is obtained by iterative linearization using successive approximation, and results for a standard numerical test case are given.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650070207
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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
    Multigrid solution and grid redistribution for convection-diffusion (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 655-664 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We examine multigrid solution for convection-diffusion problems in which convective effects are significant. In particular, we consider the case where the fine grid satisfies the associated cell or diagonal dominance condition but coarse grid levels violate this condition. Related numerical experiments are conducted. We also introduce an alternative local elliptic projection technique and compare this with interpolating the error corrections from coarse to fine grids. In addition, we demonstrate the use of grid redistribution and optimization techniques in the multilevel context.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270315
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Convergence studies of least-squares finite elements for first-order systems (1989)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 5 (1989), S. 427-434 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least-squares finite element method for first-order systems describing two-point boundary-value problems is constructed. Comparison studies are made with the corresponding mixed Galerkin formulation for the same system. Numerical experiments on representative test problems reveal that the least-squares method has superior convergence behaviour to the mixed method. Some superconvergence properties of the least-squares method are identified.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630050702
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