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  • 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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  • 2
    Electronic Resource
    Electronic Resource
    Convergence analysis of least-squares mixed finite elements (1993)
    Springer
    Computing 51 (1993), S. 111-123 
    Details
    ISSN: 1436-5057
    Keywords: 65N30 ; 65N15 ; 65L10 ; Least-squares ; mixed finite element method ; superconvergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: 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.
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02243846
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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    Superconvergence analysis of approximate boundary-flux calculations (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 483-501 
    Details
    ISSN: 0945-3245
    Keywords: 65N30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385871
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  • 5
    Electronic Resource
    Electronic Resource
    Conservation principles and variational problems (1986)
    Springer
    Acta mechanica 58 (1986), S. 93-97 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177109
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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    Electronic Resource
    Electronic Resource
    Projection and iteration in adaptive finite element refinement (1985)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 21 (1985), S. 1681-1695 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A local elliptic projection is introduced to provide improved local approximations to the finite element solution of boundary-value problems. The approach yields a composite global approximation that is more accurate and provides a good starting value for iterative solution methods. The procedure is particularly effective when used in conjunction with adaptive mesh refinement, as illustrated in numerical studies involving two-point problems of boundary-layer and interior-layer type.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620210910
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  • 10
    Electronic Resource
    Electronic Resource
    Galerkin and collocation-Galerkin methods with superconvergence and optimal fluxes (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 939-950 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element methods are formulated and investigated for the effectiveness factor problem for heat and mass transfer with chemical reactions in catalyst pellet models. A Galerkin finite element method is compared with a previous C1 collocation method7. A scheme that is conceptually intermediate between these two methods and accordingly has been termed collocation-Galerkin is formulated and numerical experiments considered. Of particular interest here are superconvergence results at the Gauss and Jacobi points, respectively. Numerical studies of superconvergence in the presence of a nonlinear reaction-rate term are presented. An integral formula is devised and used to compute the flux at the pellet surface to optimal accuracy. Numerical experiments are conducted to demonstrate the improvement in computed fluxes.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620170610
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