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  • 1
    Digitale Medien
    Digitale Medien
    Superconvergence analysis of approximate boundary-flux calculations (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 483-501 
    Details
    ISSN: 0945-3245
    Schlagwort(e): 65N30
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Certain projection post-processing techniques have been proposed for computing the boundary flux for two-dimensional problems (e.g., see Carey, et al. [5]). In a series of numerical experiments on elliptic problems they observed that these post-processing formulas for approximate fluxes were almost (O(h 2)-accurate for linear triangular elements. In this paper we prove that the computed boundary flux isO(h 2 ln 1/h)-accurate in the maximum norm for the partial method of [5]. If the solutionuφH 3(Ω) then the boundary flux error isO(h 3/2) in theL 2-norm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01385871
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Quelle: AIP Digital Archive
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.342592
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  • 3
    Digitale Medien
    Digitale Medien
    Convergence analysis of least-squares mixed finite elements (1993)
    Springer
    Computing 51 (1993), S. 111-123 
    Details
    ISSN: 1436-5057
    Schlagwort(e): 65N30 ; 65N15 ; 65L10 ; Least-squares ; mixed finite element method ; superconvergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Die Methode der kleinsten Fehlerquadrate wird bei gemischten finiten Elementen für die Differentialgleichungen erster Ordnung angewandt, die den linearen elliptischen 1-D Randwertaufgaben zweiter Ordnung entsprechen. Es werden theoretische Untersuchungen vorgestellt und Fehlerabschätzungen vorgenommen. Diese sind mit den früther von Carey and Shen [5] veröffentlichten numerischen Analysen konsistent. Die LBB Bedingung ist nicht notwendig und es werden Abschätzungen für verschiedene Grade der Austatz-Polynome vorgenommen. Superkonvergente Abschätzungen werden ebenso vorgestellt.
    Notizen: Abstract The least-squares finite element method for first order systems corresponding to second order linear two-point boundary value problems is considered. A theoretical analysis and error estimates are developed and the estimates are seen to be consistent with our previous numerical studies in Carey and Shen [5]. The method is not subject to the LBB condition and we consider, in particular, the estimates when the polynomial degree differs for the corresponding variables. Superconvergence estimates are also developed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02243846
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  • 4
    Digitale Medien
    Digitale Medien
    Basis function selection and preconditioning high degree finite element and spectral methods (1989)
    Springer
    BIT 29 (1989), S. 794-804 
    Details
    ISSN: 1572-9125
    Schlagwort(e): AMS 65F10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01932746
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  • 5
    Digitale Medien
    Digitale Medien
    Conservation principles and variational problems (1986)
    Springer
    Acta mechanica 58 (1986), S. 93-97 
    Details
    ISSN: 1619-6937
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Physik
    Notizen: Summary We show formally that integral conversation equations can be related directly to corresponding integral variational statements, without the usual appeal to the classical differential form and the associated smoothness assumptions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01177109
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  • 6
    Digitale Medien
    Digitale Medien
    Performance of iterative methods for Newtonian and generalized Newtonian flows (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 127-150 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Iterative solution ; Viscous flow ; Generalized conjugate gradient ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: We consider the use of accelerated gradient-type iterative methods for solution of Newtonian and certain non-Newtonian (power-law and Bingham models) viscous flow problems. The formulations are based on penalty and mixed finite element methods, and such factors as the effect of the penalty parameter, asymmetry, continuation and preconditioning are examined.
    Zusätzliches Material: 19 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650090202
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  • 7
    Digitale Medien
    Digitale Medien
    On the computed pressures for Navier-Stokes problems at increasing Reynolds numbers using the penalty finite element method (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 439-442 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650050504
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  • 8
    Digitale Medien
    Digitale Medien
    Local pressure oscillation and boundary treatment for the 8-node quadrilateral (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 165-172 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Pressure Oscillations ; Driven Cavity ; Boundary Data ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: The 8-node (serendipity) velocity basis with C° bilinear pressure is a popular element but has been observed to yield poor pressures. We present some details of numerical experiments that indicate the local nature of the error and the effects of mesh refinement, increasing Reynolds number and regularity of the data. This leads to a strategy for appropriately modifying the data near the corners that is effective in improving the computed pressure approximation.
    Zusätzliches Material: 8 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650060306
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  • 9
    Digitale Medien
    Digitale Medien
    Turbulent boundary-layer analysis using finite elements (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 769-787 
    Details
    ISSN: 0271-2091
    Schlagwort(e): Turbulent Boundary Layer ; Kκ-ε Model ; Dorodnitsyn Finite Element ; Heat Transfer ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: The use of finite element methods for turbulent boundary-layer flow is relatively recent and of limited extent.1 In the present study, we extend the group variable approach of Fletcher and Fleer2,3 to treat turbulent boundary layer flows with heat transfer using a two-equation turbulence model. The main concepts in the formulations include a Dorodnitsyn-type transformation which uses a velocity component as the transverse variable, a ‘variational’ formulation for the transformed equations using special test functions and development of a two-equation turbulence model in terms of the turbulent kinetic energy and turbulence dissipation rate as additional field variables. Several numerical test cases have been examined comparing the results with finite difference calculations and comparing the two-equation turbulence model with an algebraic turbulence model.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650061102
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  • 10
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Finite Elements ; Interface Penalties ; Viscous Flow ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: 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.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/fld.1650070207
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